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Statistics homework help

STATISTIC FINAL PROJECT 1

Reporting a systematic review or meta-analysis.

Instructions:

Questions 1-27 in appendix 1 need to answered. The questions can be answered in like a table format. Questions on one side and answers on the other one or questions on top and answers below.

Most of the answers are on the written report that start on page 4-15, in the different sections, but I’m including the research articles for additional reference.

Questions apply to the 4 article on the literature review. (Badu et al., 2020), Hu et al. (2020), Dharra & Kumar, (2021), (Yao et al., 2018). So when you answer them, you can do it in a narrative style individually Like

A. answer for article 1

B. answer for article 2

C. …

D. …

Or just one answer that covers all of them if they have the same outcome/response.

Appendix 1

Checklist of items to include when reporting a systematic review or meta-analysis.

Section/Topic

#

Checklist Item

Reported on Page #

TITLE

Title

1

Identify the report as a systematic review, meta-analysis, or both.

ABSTRACT

Structured summary

2

Provide a structured summary including, as applicable: background; objectives; data sources; study eligibility criteria, participants, and interventions; study appraisal and synthesis methods; results; limitations; conclusions and implications of key findings; systematic review registration number.

INTRODUCTION

Rationale

3

Describe the rationale for the review in the context of what is already known.

Objectives

4

Provide an explicit statement of questions being addressed with reference to participants, interventions, comparisons, outcomes, and study design (PICOS).

METHODS

Protocol and registration

5

Indicate if a review protocol exists, if and where it can be accessed (e.g., Web address), and, if available, provide registration information including registration number.

Eligibility criteria

6

Specify study characteristics (e.g., PICOS, length of follow-up) and report characteristics (e.g., years considered, language, publication status) used as criteria for eligibility, giving rationale.

Information sources

7

Describe all information sources (e.g., databases with dates of coverage, contact with study authors to identify additional studies) in the search and date last searched.

Search

8

Present full electronic search strategy for at least one database, including any limits used, such that it could be repeated.

Study selection

9

State the process for selecting studies (i.e., screening, eligibility, included in systematic review, and, if applicable, included in the meta-analysis).

Data collection process

10

Describe method of data extraction from reports (e.g., piloted forms, independently, in duplicate) and any processes for obtaining and confirming data from investigators.

Data items

11

List and define all variables for which data were sought (e.g., PICOS, funding sources) and any assumptions and simplifications made.

Risk of bias in individual studies

12

Describe methods used for assessing risk of bias of individual studies (including specification of whether this was done at the study or outcome level), and how this information is to be used in any data synthesis.

Summary measures

13

State the principal summary measures (e.g., risk ratio, difference in means).

Synthesis of results

14

Describe the methods of handling data and combining results of studies, if done, including measures of consistency (e.g., I2) for each meta-analysis.

Risk of bias across studies

15

Specify any assessment of risk of bias that may affect the cumulative evidence (e.g., publication bias, selective reporting within studies).

Additional analyses

16

Describe methods of additional analyses (e.g., sensitivity or subgroup analyses, meta-regression), if done, indicating which were pre-specified.

RESULTS

Study selection

17

Give numbers of studies screened, assessed for eligibility, and included in the review, with reasons for exclusions at each stage, ideally with a flow diagram.

Study characteristics

18

For each study, present characteristics for which data were extracted (e.g., study size, PICOS, follow-up period) and provide the citations.

Risk of bias within studies

19

Present data on risk of bias of each study and, if available, any outcome-level assessment (see Item 12).

Results of individual studies

20

For all outcomes considered (benefits or harms), present, for each study: (a) simple summary data for each intervention group and (b) effect estimates and confidence intervals, ideally with a forest plot.

Synthesis of results

21

Present results of each meta-analysis done, including confidence intervals and measures of consistency.

Risk of bias across studies

22

Present results of any assessment of risk of bias across studies (see Item 15).

Additional analysis

23

Give results of additional analyses, if done (e.g., sensitivity or subgroup analyses, meta-regression [see Item 16]).

DISCUSSION

Summary of evidence

24

Summarize the main findings including the strength of evidence for each main outcome; consider their relevance to key groups (e.g., health care providers, users, and policy makers).

Limitations

25

Discuss limitations at study and outcome level (e.g., risk of bias), and at review level (e.g., incomplete retrieval of identified research, reporting bias).

Conclusions

26

Provide a general interpretation of the results in the context of other evidence, and implications for future research.

FUNDING

Funding

27

Describe sources of funding for the systematic review and other support (e.g., supply of data); role of funders for the systematic review.


The actions for prevention in the workplace to reduce nurse burnout

The term burnout was considered in 1974 after observing a lack of motivation and decreased commitment among volunteers at a mental health clinic. The current definition of burnout syndrome is “a constant exposure to stress during the work time, and associated with inadequate working conditions, that results in decreased pleasure and work performance.” Some professionals can manage the symptoms, but those who do not adapt to the working conditions, lack of work force, and poor communication frequently feel physically and psychologically exhausted, and they will suffer from burnout syndrome in the longer term. Nurses’ ability to provide care is hampered by burnout (Dall’Ora et al., 2020).

Background

Burnout Syndrome (SB) is considered a consequence of professional stress. It is distinguished by a reaction to long-term socioemotional and interpersonal stressors at work. In this context, work stress is defined as the body’s adaptive response to new situations, particularly those regarded as threatening. Nursing burnout is a major threat to the healthcare system of the United States. Nurses are the largest section of our healthcare workforce, accounting for nearly thirty percent of hospital employment in 2019 (Shah et al., 2021).

It is considered that the demands on health care systems (HCS) and clinicians have risen, so have the expectations and requirements placed on nurses, which has a negative impact on their working environment. When combined with the ever-increasing stress caused by the COVID19 disease, this scenario may leave the United States with a fluctuating nursing workforce for the years to follow. Given their diverse skill set, significance on the care team, and percentage of the health care workforce, it is critical that we gain a better understanding of job-related consequences and the contributing factors to nursing staff burnout across the country (Shah et al., 2021). The purpose of this project is to research about the causes of nursing burnout, and the actions for prevention in the workplace.

Statement of the Problem and Purpose of the Study

Much research has been conducted on the phenomenon of excessive workload and burnout, and nurses stand out as one of the most vulnerable professional groups at risk of burnout (Kowalczuk et al., 2020). The occurrence of a pandemic that affect the whole work, has emerged as a big problem the burnout, health system has been affected to address a high-quality service and burnout specific in nurses has increase the prevalence of this problem. The purpose of this project is to conduct research of the causes of nursing burnout, and the actions for prevention in the workplace.

This research will examine the causes, implications, and preventative measures of nursing burnout syndrome in the nursing area and discovered that a continuous search for more comprehensive solutions is required. These solutions must come from system-level actions to reinvent and innovate work – flow, human resource management, and workplace wellbeing, to eliminate or reduce nurse burnout and work forward into healthier healthcare professionals, better healthcare, and reduced costs.

Research Questions, Hypothesis, and Variables with Operational Definitions

Research Question

Do the actions for prevention in the workplace reduce nurse burnout?

Hypothesis: Research and Null

Null hypothesis:

The actions for prevention in the workplace reduce nurse burnout.

Alternative hypothesis

The actions for prevention in the workplace do not reduce nurse burnout.
Identifying and Defining Study Variables

Through literature review, the author will explore the following variables:

· Prevalence of burnout.

· Age.

· Nurse specialties include staff nurses, midwives, nurse practitioners, and registered nurses and managers who worked in the main specialties.

Operationalize Variables, that will consider with the inclusion and exclusion criteria to select the literature.

Burnout measure based on the Maslach Burnout Inventory (MBI) (Maslach & Leiter, 2016), that has been validate and is based in:

1. Emotional Exhaustion quantifies sentiments of being emotionally overburdened and exhausted by one’s job.

2. Depersonalization assesses an unfeeling and indifferent reaction to patients.

3. Personal Accomplishment assesses emotions of competence and accomplishment in one’s employment.

Synthesis of Literature review

Kleinpell et al. (2020) published an updated article from the Critical Care Societies with the highlights prevention and management of burnout (BS) within the intensive care unit (ICU). The Societies explained how burnout has serious ramifications for workplace morale, patient safety, quality of care, and healthcare expenses, significant costs related to practitioner turnover. The analysis has shown that all care suppliers are at risk of burnout. Also, crucial care clinicians are more vulnerable. consistent with recent surveys, intensivists have the highest rate of BS t of any specialty, and critical care nurses have additionally been evidenced to have significant rates of burnout, that does not have only one simply known cause; rather, a range of variables may contribute to that, one of the main drivers of burnout in health care is that the accumulated clerical burden, that is due to partially to electronic medical history documentation standards (Kleinpell et al., 2020).

Yao et al. (2018) examined the links between job-related BS, stress, general self-efficacy, and personality types, additionally as how they move in job-related BS. Nurses suffer from burnout, which may be a health issue. individuals with specific personalities are additional at risk of job-related burnout. GSE (general self-efficacy) may be a vital predictor of job-related burnout. The connections between general self-efficacy, job-related burnout, and different temperament types are still unclear (Yao et al., 2018).

The study (Yao et al., 2018) was designed as a cross-sectional survey of 860 nurses in China. The measured variables included the nurses’ job-related burnout using the scale of the Maslach activity Burnout Scale (MABS), and personality, stress, and GSE. The authors conclude that the highest causes of job-related burnout are stress, GSE, and introspective unstable temperament. The GSE reduces the impact of stress on burnout in nurses with sociability or neurosis. Reducing stress, enhancing GSE, and increasing social support might facilitate nurses avoid job-related burnout. Nurses with introspective unstable personalities need assistance to cut back stress and improve their GSE (Yao et al., 2018).

Dharra & Kumar, (2021) analysis concerning GSE is thought of as one of the foremost important factors which will modify the impact of tension on nurses’ psychological state. within the study, the authors’ aimed to work out the predictors of self-efficacy and anxiety among nurses throughout this COVID-19 pandemic. The study consisted in a cross-sectional survey involving 368 nurses operating in tertiary care hospitals. The General Self-Efficacy scale (GSE) and Generalized anxiety disorder Scale-7 (GAD-7) were used for assessing self-efficacy and anxiety . The authors affirm that adequate COVID-19 training is crucial for reinforcing self-efficacy and reducing anxiety among nurses throughout the continued pandemic, conjointly that managing anxiety, enhancing self-efficacy, and increasing exposure to COVID-19-related coaching might improve nurses’ psychological state and higher prepare them to fight pandemics (Dharra & Kumar, 2021).

Another author, Hu et al. (2020) published the results of a study that examine psychological state (burnout, anxiety, depression, and fear) and their associated factors among frontline nurses caring for COVID-19 patients in urban center, China. The study enclosed a complete of 2,014 frontline nurses from 2 hospitals in Wuhan, China, who participated in the study. The people experienced substantial burnout and a big level of worry. Emotional temporary state in 60.5 percent, depersonalization in 42.3 %, and personal accomplishment in 60.6 percent. The other characteristics (tension, despair, and terror) were respectively per the data, 14.3 percent, 10.7 percent, and 91.2 % of nurses knowledgeable moderate to high degrees (Hu et al., 2020).

Another author (Badu et al., 2020) revealed a review that integrated each qualitative and quantitative information into one synthesis. The authors report as contributing issues of stress among workplace nurses: workplace bullying, depression, and anxiety, the evidence indicates that Australian nurses experience moderate to high levels of stress, which is related to workplace bullying. These nurses additionally had moderate to high levels of depression and anxiety, further as burnout. This review concludes that many individual attributes and structure (environmental) resources are used as varieties of resilience to manage workplace adversity (Badu et al., 2020).


Research design and methods

Sampling

The methods used in literature review research design is different from other research designs because rather than patients, data to write the report are collected from the published literature (Goldberg, 2020). The sampling plan include articles, the literature review represents a method because during the process it occur a choose from an array of strategies and procedures for identifying, recording, understanding, meaning-making, and transmitting information pertinent to a topic of interest (Goldberg, 2020).

The sample of the articles for the project will be selected through a search process in database with criteria of inclusion and exclusion. At least 10 primary articles from peer-reviewed journals, that has been published between 2017 to 2021, to be consistent with the research question that will compare the information about prevalence of burnout before and after COVID pandemic.

The sampling methods used for this project will be a non-probability sampling because is related to articles that will evaluated to adequate or not for to answer the research question, and involves non-random selection based on convenience or other criteria (Berndt, 2020). This sampling method is appropriate for the type of study for the purpose of student project, that is through literature review, select articles that give information about prevalence, and other topics in burnout before and after the pandemic.

This type of non-probabilistic sample is adequate for the research design of the narrative review that will be used. A priori, the student project to review at least 10 articles, the number of literatures that will be search will account a big number, approximately in a primary search with the key word burnout covid and nurse in PubMed give 61 articles, that is only with two key word and only one data base, in that case, 10 articles will be approximately 16.6 percent of the PubMed results.

To ensure a systematic review is valuable to users, principal investigator will prepare a transparent, complete, and accurate account of why the review was done, what they did (such as how studies were identified and selected) and what they found (such as characteristics of contributing studies and results of meta-analyses)

The research design will flow from the proposed research problem, theoretical framework, literature review, and hypothesis, with the aspect suggested in table 1.

Table 1:

Flow from the proposed research problem

Background concepts

New concepts

Applying concepts

Data collection (literature)

Selection of articles

Type of articles (quantitative/qualitative)

Prevalence of burnout in nursing during Covid pandemic.

Literature review

Theoretical Framework

Variables

According to Manzano-García & Ayala, (2017), burnout is not only caused by work-related factors. For the research, other factors such as lifestyle and personality traits will also consider if there is available quantitative or qualitative evidence to included and adjust the prevalence rate (Manzano-García & Ayala, 2017).

The project will consider two extraneous variables: Lifestyle and personality traits. A counterbalancing will be selected as a method to control extraneous variables, reviewing the order of events of burnout in the study, this means that we will report the event that appear first, if the personality trait, or the burnout that could affect the nurse practitioner independently of the personality trait. The personality trait that are reported in literature associated to burnout are neuroticism that increased the vulnerability to perceived stress and burnout, whereas traits of extraversion, conscientiousness, and agreeableness were protective against perceived stress and burnout. Then any of this personality trait will be control as a dichotomous variable of present or not present.

Instrument

The Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) as instrument for literature review, the checklist includes 27 reporting items (Appendix 1 ). The title, abstract, methods, results, discussion and funding each of which is detailed and will be used to the analysis (Moher et al., 2009).

Level of measurement for literature review (nominal)

As a result, a five-step approach will be employed to undertake a scoping review:

1) Identifying a research issue; 2) Identifying relevant studies; 3) Choosing relevant studies; 4) Charting the data; and 5) Collecting, summarizing, and publishing the results. To end the process: Summarize the key findings and connect them to the original review questions and objectives (Sidhu et al., 2020).

For the evaluation of burnout, the instrument that will be used is the Maslach Burnout Inventory (MBI), that use a scale of emotional exhaustion, depersonalization, and personal accomplishment, which is the most widely validate and used measurement for evaluating burnout syndrome (Wang et al., 2020).

For this research, the literature will be classified in

1. Burnout Syndrome rate among nurses (RN and NP) and health care professional reports before the COVID-19 pandemic (year 2020).

2. Burnout Syndrome rate among nurses (RN and NP) and health care professional reports after the COVID-19 pandemic (year 2020).

3. The uses of stress management strategies are effective in decreasing burnout in nurses and other healthcare staff.

4. Tactics to help reducing burnout in health care professionals (Colleague support, workout, positive attitude outlook on life).

The PRISMA statement (Appendix 1) will be applied to assess the quality of reporting. Each item will be assessed as follows: ‘Yes’ for total compliance, scored ‘1’; ‘partial’ for partial compliance, scored ‘0.5’; and ‘No’ for non-compliance, scored ‘0’.

Data collection procedure

Data collection would include distributing forms to collect important data of the literature review. In terms of literature review the data collection is referred to as “charting the data”. The aim is to create a descriptive summary of the results which addresses the scoping review’s objectives, and ideally answers the questions of the review (research question) (Delaney, 2021). The results of the collection of data will be presented in tables with the essential information extracted from each article. Figure 1 show a diagram of the whole process.

Level of measurement

Burnout syndrome will consider is it was measured using the Maslach Burnout Inventory (MBI) that comprises 22 items with a seven-point Likert response scale from zero (‘‘Never’’) to six (‘‘Every day’’). The MBI has three dimensions: emotional exhaustion (EE; nine items), depersonalization (D; five items) and personal accomplishment (PA; eight items) , MBI is the most widely validate and used measurement for evaluating burnout syndrome (Wang et al., 2020). The level of measurement is nominal.

Data analysis plan

The data for demographic information (age, gender, occupation, marital status, years of practice, working hours per day, and education level) will be review if has been collected in the selected articles, and the analysis according to the type of variable, for scale variable: age, years of practice, working hours per day will be express using summary measures as mean, median and standard deviation will be use. For nominal variables, frequency, and percentage (See diagram 1). All data will be selected from the articles that has been included in the project, additional articles could be added during the research process if more recent literature is available with newer information.

Limitation of Proposed Study

There are an overwhelming number of assessment tools available in the literature that can be used to measure the different components of nurse’s well-being. While our literature search was methodical and broad, we acknowledge that we may have missed some key assessment tools. At times, only the principal investigator will determine the inclusion eligibility of the tools identified in the reviewed literature. This type of research that included a systematic review is recommended that two authors review each article.



Implications and contributions to knowledge

In this project, it might consider that how the actions for prevention in the workplace reduce nurse burnout, we will determine and compare the prevalence of nurse burnout before and after COVID-19. The strategies for the solution of burnouts need to be adapted in place, following the guidelines of workforce, we agree that the unprecedented Covid-19 pandemic signified a profound impact on nursing and healthcare services. The health professional knows that the need for compassionate nurses and healthcare workers is critical.


Figure 1.

# of records identified through database searching

# of additional records identified through other sources

# of records after duplicates removed

# of records screened

# of records excluded

# of full-text articles assessed for eligibility

# of studies included in qualitative synthesis

# of full-text articles excluded, with reasons

# of studies included in quantitative synthesis (meta-analysis)

Included

Eligibility

Identification

Screening

Diagram of the methodology for the study.


References

Badu, E., O’Brien, A. P., Mitchell, R., Rubin, M., James, C., McNeil, K., Nguyen, K., & Giles, M. (2020). Workplace stress and resilience in the Australian nursing workforce: A comprehensive integrative review. International Journal of Mental Health Nursing, 29(1), 5–34. https://doi.org/10.1111/inm.12662

Berndt, A. E. (2020). Sampling Methods. Journal of Human Lactation, 36(2), 089033442090685. https://doi.org/10.1177/0890334420906850

Dall’Ora, C., Ball, J., Reinius, M., & Griffiths, P. (2020). Burnout in nursing: a theoretical review. Human Resources for Health, 18(1). https://doi.org/10.1186/s12960-020-00469-9

Dharra, S., & Kumar, R. (2021). Promoting Mental Health of Nurses During the Coronavirus Pandemic: Will the Rapid Deployment of Nurses’ Training Programs During COVID-19 Improve Self-Efficacy and Reduce Anxiety? Cureus. https://doi.org/10.7759/cureus.15213

Goldberg, J. (2020). LibGuides: Conducting Research in the Health Sciences: Narrative Literature Reviews. Simmons.libguides.com. https://simmons.libguides.com/c.php?g=371871&p=2516196

Hu, D., Kong, Y., Li, W., Han, Q., Zhang, X., Zhu, L. X., Wan, S. W., Liu, Z., Shen, Q., Yang, J., He, H.-G., & Zhu, J. (2020). Frontline nurses’ burnout, anxiety, depression, and fear statuses and their associated factors during the COVID-19 outbreak in Wuhan, China: A large-scale cross-sectional study. EClinicalMedicine, 0(0). https://doi.org/10.1016/j.eclinm.2020.100424

Kleinpell, R., Moss, M., Good, V. S., Gozal, D., & Sessler, C. N. (2020). The Critical Nature of Addressing Burnout Prevention. Critical Care Medicine, 48(2), 249–253. https://doi.org/10.1097/ccm.0000000000003964

Kowalczuk, K., Krajewska-Kułak, E., & Sobolewski, M. (2020). Working Excessively and Burnout Among Nurses in the Context of Sick Leaves. Frontiers in Psychology, 11. https://doi.org/10.3389/fpsyg.2020.00285

Manzano-García, G., & Ayala, J.-C. (2017). Insufficiently studied factors related to burnout in nursing: Results from an e-Delphi study. PLOS ONE, 12(4), e0175352. https://doi.org/10.1371/journal.pone.0175352

Maslach, C., & Leiter, M. P. (2016). Understanding the burnout experience: recent research and its implications for psychiatry. World Psychiatry, 15(2), 103–111. https://doi.org/10.1002/wps.20311

Shah, M. K., Gandrakota, N., Cimiotti, J. P., Ghose, N., Moore, M., & Ali, M. K. (2021). Prevalence of and Factors Associated With Nurse Burnout in the US. JAMA Network Open, 4(2), e2036469. https://doi.org/10.1001/jamanetworkopen.2020.36469

Wang, J., Wang, W., Laureys, S., & Di, H. (2020). Burnout syndrome in healthcare professionals who care for patients with prolonged disorders of consciousness: a cross-sectional survey. BMC Health Services Research, 20(1). https://doi.org/10.1186/s12913-020-05694-5

Yao, Y., Zhao, S., Gao, X., An, Z., Wang, S., Li, H., Li, Y., Gao, L., Lu, L., & Dong, Z. (2018). General self-efficacy modifies the effect of stress on burnout in nurses with different personality types. BMC Health Services Research, 18(1). https://doi.org/10.1186/s12913-018-3478-y


Statistics homework help

EDCO 745

Part 1

REGRESSION DATA SCREENING OUTPUT ASSIGNMENT INSTRUCTIONS
OVERVIEW
Data screening is fundamental prior to any analysis. The basics of data screening are outlined in
your Warner text. This is the third time you will do data screening.

INSTRUCTIONS
1. Using data based upon the topic, instruments, and variables selected in your models you have
developed in Modules 5 and 6, turn in your data screening output for regression analysis. (Please note: My topic was depression)
Note: You only have to turn in output for data screening of the variables you use in your analysis.
Output should include:
• Variable Selections
• Frequencies
• Crosstabs (if necessary)
• Boxplots (if necessary)
• Scatterplot
Note: Your assignment will be checked for originality via the Turnitin plagiarism tool.

Part 2

Model Drawings Assignment Instructions

Overview

• Learning to conceptualize your analysis in drawings helps communicate your ideas. Using Hayes models as a starting point is a useful way to conceptualize the variables of interests and their causal sequence.

Instructions

Turn in at least two proposed models.

• These models must be based on Hayes’ models in his currently published text

• Use your variables of interest to construct your models

• For each model, include a brief description of the model

• Include a title page and reference page

** Refer to Model 4 Write-up Document (file in Module: Week 6 folder) for more information on this assignment.**

Model 4 is commonly referred to as the Simple Mediation Model.

Note: Your assignment will be checked for originality via the Turnitin plagiarism tool.

Statistics homework help

Directions:  For the earlier projects in this class, I asked you to go out and perform an experiment and then write about it.  This time, it’s a library exercise.

Find a news article related to recent developments in some type of science, whether medicine, social science, physics, or something else.  You can find it in a newspaper, magazine, or on the Internet, but if you use the Internet, the source must be a real media company (nytimes.com, foxnews.com, etc).

Your task is to critique the article.  Not just to summarize or interpret it, but to figure out what might be wrong with it.  You might have to look through several articles to pick out one with interesting mistakes or problems.

You should question the source, methods, results, and conclusion.

1) Question the source.  If the article is about a recent study or experiment, then who did the study?  Are they impartial?  Or biased?  Who paid for the study?  If it was a study of a product paid for by the manufacturer, the results might be overly rosy.  If it was a nonprofit group or foundation, what are their political leanings or prejudices?

2) Question the methods.  If the article tells you about how the study was conducted, decide whether or not it was done well.  Does the author describe how the sample was selected?  If it was a survey, how were the questions phrased?  If the article doesn’t tell you these things, that’s a weakness.

3) Question the results.  What was the sample size?  Was it large enough?  Does the article talk about margin of error?  Is it possible that the apparently interesting results could be a coincidence?

4) Question the conclusion.  What did the scientists really find, and what are the headlines saying?  Remember correlation is not causation—just because two things tend to happen at the same time does not mean that one causes another.

Please show me your article as soon as you select it, so I can confirm that it is a good choice.  Make sure that it’s long enough to provide some meat, but not so long and technical that you don’t understand it.  When you submit your final project, include a link to or copy of the original article.

Statistics homework help

Chapter 10 Data Mining

Instructions: Please submit your work in one single Excel file with one tab/worksheet for each problem.

Cluster Analysis

1. (25 points) Apply single linkage cluster analysis to Berkeley, Cal Tech, UCLA, and UNC in the Excel file Colleges and Universities Cluster Analysis Worksheet and draw a dendrogram illustrating the clustering process.

Classification

2. In the Excel file Credit Risk Data, classify the following record:

a. (25 points) Using k-NN algorithm for k=1 to 5.

b. (25 points) Using discriminant analysis.

Association

3. (25 points) The Excel file Automobile Options provides data on options ordered together for a particular model of automobile. Consider the following rules:

a. Rule 1: If Fastest Engine, then Traction Control.

b. Rule 2: If Faster Engine and 16-inch Wheels, then 3 Year Warranty.

Compute the support, confidence, and lift for each of these rules.

Statistics homework help


Coffee consumption and heart health Sep 17, 2020

Coffee is one of the most consumed beverages worldwide.  It’s hard to beat a good cup of coffee – especially as the weather begins to turn cooler.  But what about coffee consumption and heart health?  A meta-analysis (a quantitative, systematic study to assess results of previous research) of 36 long-term research studies was conducted to determine the relationship of long-term coffee consumption and risk of cardiovascular disease.  The combined participants in these studies were approximately 1.2 million and the average length of follow-up was ten years.  This meta-analysis found that drinking 3.5 cups of coffee per day (caffeinated or decaffeinated) was associated with a 15% lower risk of cardiovascular disease compared to drinking no coffee (Ding, et al., 2014). 

A Swedish study followed a cohort of 1369 patients for eight years after being hospitalized for a first heart attack.  This study found that those who drank two or more cups of caffeinated coffee per day were 40% less likely to die from cardiovascular disease than those who drank none or only one cup of coffee per day (Mukamal, et al., 2009).   A more recent study of a cohort of 4365 Dutch patients who had a previous heart attack found that drinking coffee (either caffeinated or decaffeinated) was associated with a lower risk of death from both cardiovascular disease and ischemic heart disease (Dongen, et al., 2017).  

It is important to keep in mind that a standard cup of coffee is about six ounces.  A coffee mug can hold much more than six ounces of coffee.  In fact, some large mugs may be equivalent to two or more six-ounce cups of coffee.  Be sure to limit added sugars and creamers, as these can quickly add up in extra calories. 

It is also important to note that unfiltered coffee contains cafestol and kahweol.  These two compounds are associated with increased levels of cholesterol and triglycerides.  Cafestol and Kahweol are mostly removed when coffee is filtered with a paper filter (Du, et al., 2020).  

  While many studies have found an association between coffee consumption and reduced cardiovascular disease, this does not mean that consumption of coffee causes a reduced risk of cardiovascular disease.  In other words, in research, association does not prove cause and effect.  In addition, individual sensitivity to caffeine can vary considerably.  It is especially important that individuals with a history of heart disease and those taking medications for heart disease always check with their physician before making significant changes in caffeine consumption.  

Sources:

Ding, M., Bhupathiraju, S. N., Satija, A., Van Dam, R. M., Hu, F. B. (2014).  Long-term coffee consumption and risk of cardiovascular disease.  Circulation, 129, 643-659. 

Dongen,  L. H., Mölenberg, F. JM., Soedamah-Muthu, S. S., Kromhout, D., Geleijnse, J. M. (2017).  Coffee consumption after myocardial infarction and risk of cardiovascular mortality: A prospective analysis in the Alpha Omega Cohort, The American Journal of Clinical Nutrition, 106 (4), 1113–1120, https://doi.org/10.3945/ajcn.117.153338

Du Y, Lv Y, Zha W, Hong X, Luo Q, (2020).  Effect of coffee consumption

on dyslipidemia:  A meta-analysis of randomized controlled trials.  Nutrition, Metabolism and Cardiovascular Diseases.  https://doi.org/10.1016/j.numecd.2020.08.017.

Mukamal KJ, Hallqvist J, Hammar N, et al. (2009).  Coffee consumption and mortality after acute myocardial infarction: The Stockholm Heart Epidemiology Program.  American Heart Journal, 157(3):495-501. doi:10.1016/j.ahj.2008.11.009

https://www.djournal.com/pontotoc/coffee-consumption-and-heart-health/article_a0bb9517-46db-5155-ab51-e18af3062508.html

Statistics homework help

Chapter 12 Simulation and Risk Analysis

Instructions: Please submit your work in one single Excel file with one tab/worksheet for each problem.

1. (50 points) In class, we developed a simple spreadsheet model for computing profit in Excel. Use this profit model to implement a financial simulation model for a new product proposal and determine a distribution of profits using the discrete distribution below for the demand, unit cost, and fixed cost. Price is fixed at $1,000. Demand is unknown and follow the distribution:

Demand

Probability

120

0.25

140

0.50

160

0.25

Unit costs are also variable and follow the following distribution:

Unit Cost

Probability

$400

0.20

$600

0.40

$700

0.25

$800

0.15

Fixed costs are estimated to follow the distribution:

Fixed Costs

Probability

$45,000

0.20

$50,000

0.50

$55,000

0.30

Simulate this model for 50 trials and a production quantity of 140. What is the average profit?

2. (50 points) J&G Bank receives a large number of credit card applications each month, an average of 30,000 with a standard deviation of 4,000, normally distributed. Approximately 60% of them are approved, but this typically varies between 50% and 70%. Each customer charges a total of $2,000, normally distributed, with a standard deviation of $250, to his or her credit card each month. Approximately 85% pay off their balances in full, and the remaining incur finance charges. The average finance charge has recently been ranged from 3% to 4% per month. The bank also receives income from fees charged for late payments and annual fees associated with the credit cards. This is a percentage of totally monthly charges and has varied between 6.8% and 7.2%. It costs the bank $20 per application, whether it is approved or not. The monthly maintenance cost for credit card customers is normally distributed with a mean of $10 and standard deviation of $1.50. Finally, losses due to charge-offs of customers’ accounts are between 4.6% and 5.4% of total charges. Use Monte Carlo simulation with 500 trials to analyze the profitability of the credit card product.

Statistics homework help

Fleming Mwashako Mwalugho

Sheffield Hallam

Research

Introduction

High sodium content is a global issue. Most countries have enacted laws to help curb the sodium content in food. However, some of the enactments are not fully enforced exposing the food industry to high food sodium especially in processed food and in certain cuisines. It is now established that high salt content leads to an increase in blood pressure and greatly increases the risk for cardiovascular diseases. According to (Du et al., 2022) cardiovascular diseases are one of the leading causes of death in most western countries accounting for more than 30% of the deaths. It is widely accepted that the consumption of high sodium foods is above the Food Standard Agency (FSA) recommended levels in the United Kingdom.

The WHO targets a 30% of salt reduction by 2025 with an adult consumption recommendation of fewer than 5 grams of salt per day. The United Kingdom set a target to reduce salt content for more than 85% of food categories ten years ago and this resulted in more than 20% reduction in high blood pressure and cardiovascular disease-related deaths. In China, intake of sodium is very high ranging from 12-14g/d, this is accompanied by the increase in the consumption of sauces like soy sauce which account for the highest rates, and processed food that also has high sodium content. This is also witnessed in the UK where most urban populations indulge in foreign cuisines. In developed countries, it is estimated that processed foods account for more than 75% of the salt consumed (Tan et al., 2019). Studies have shown that Chinese food, ingredients, and accompaniments in the United Kingdom contain higher levels of sodium than recommended by the FSA 2024 (Tan et al., 2019). Further in a study that was conducted in 2017 most UK products met the FSA standards but only 13% of Chinese products met the recommended FSA standards for sauces and Ingredients. Studies have demonstrated that it is possible to reduce salt content in Chinese food. Following the enactment of policies in past on salt regulation in the UK, there is a substantial decrease in the sodium content in Chinese cuisines this is in comparison to china where the same products are consumed. The most important strategy in reducing salt consumption is identifying the amount of salt consumed and how it is consumed. The aim of the study was to establish the sodium content in Chinese meal components, ingredients, and sauces and to determine if they are in line with the FSA 2024 standards. The final report provides actual values of salt content and helps in reviewing targets and informing consumer decisions. This was achieved by systematically collecting data on sodium levels on the UK processed Chinese products and comparing the sodium values against the UK FSA 2024 standard on salt content.

Literature review

He & MacGregor (2018) in a research on the relationship between high salt intake and cardiovascular diseases propose that a high level of sodium in food is highly detrimental and takes a toll on the life of a person. They explain that high sodium in foods increases the risk of hypertension which is dangerous, especially for people with comorbidities. The above argument is further supported by Bandy et al (2021) in research on U.K food safety and sodium levels found that high sodium levels increased the risk of cardiovascular diseases, hypertension, renal diseases, and stroke by 55% in a sample population of 1045 on a study conducted between 2019 and 2021. A study conducted by (Barton et al., 2011) raised blood pressure accounted for 47% of strokes and this is linked to evidence that high consumption levels of salt consumed in diets is the leading cause for high blood pressure.

Elsewhere Rippin et al., (2019) in a research on the effects of high sodium levels in energy foods in the UK by use of urinary sodium surveys, also found that the risk of hypertension and stroke was increased by 49% in a study sample size of 2200 drawn from various age groups. Additionally, the study also revealed, that 76% of the sodium taken was drawn from processed foods. The above therefore creates the need to investigate sodium levels in foods in the UK if they are in line with the F.S.A 2024 standards.

Antúnez et al., (2019) in a research on the F.S.A guidelines and standards on foods, explains various standards. Among the main findings is that there are various subcategories of targets to be met by food manufacturers by 2024. For instance, slices of bacon are set at 1035 sodium (2.59g of sodium) per 100 grams of bacon and 430mg sodium (1.08g sodium) per 100 grams of sausages. Tan et al., (2019) in research on the same, support the above findings by further giving more targets as set out by the F.S.A. further, the author lists and explains the targets like meat pies with a target of 370 mg sodium (0.93 sodium) per 100 gram of meat pie and standard of 320mg sodium (0.8g salt) for meat-based pasties by 2024.

Menyanu, Russell & Charlton (2019) further in their discussion they expound more on the above standards by discussing several standards and their anticipated importance. Among the foods standards the writers discuss are the above and more such as pizza, soups, crisps, snacks and biscuits. Sampling the standards, the target for biscuits is 220 mg sodium (0.55g salt) and for children’s main meals is 685 mg sodium (1.71g salt) per 100 mg of their food. The authors further posit that the above targets are part of the campaign started in 2003 by the F.S.A to reduce salt intake to 6mg per day per person by 2024.

Zhang et al., (2020) in research on Chinese processed foods, argues that Chinese processed foods are among the most popular cuisines in the U.K. additionally the writer argues that Chinese foods are four-fold saltier and higher in sodium in the U.K. Tan et al., (2019) further agree with the above by discussing that Chinese foods have high salt levels with an average of 13 g per day. Additionally, he explains that Chinese products such as sauces account up to 6% of total salt levels.

He et al., (2018) in their research reaffirms the above findings through research on Chinese salt and sodium levels research conducted in 2018-2019. In the study findings, the Chinese cuisine had more salts than the U.K foods. Specifically, from the researcher’s findings on instant noodles, of 10 sampled, 4 had more salt levels as compared to 2 of the U.K noodles. Additionally, 8 out of 11 food groups in China had more salt and sodium content compared to the same sampled in the UK. On average the writer affirms that Chinese products mostly non-processed had 4.5 times more salt than those from U.K. The comparison was done largely on non-processed and large groups of processed foods with little focus on processed foods.

In the longitudinal study conducted by (Ni Mhurchu et al., 2010) there was high sodium content in the food served in UK households. More than 50% of the salt consumed was added as table salt (Ni Mhurchu et al., 2010). The other 50% was mainly salt added at the point of processing ready meals. With the increase in ready meal consumption, there has been a substantial increase in dietary sodium levels in the UK (Ni Mhurchu et al., 2010). The intake of Chinese food from supermarkets has also increased over time reducing the gains that were instituted by the FSA in 2004.

In the UK the FSA recommends the reduction of salt intake to 6 grams in adults, it is also estimated that 75% of salt intake is derived from the consumption of processed foods retailed in supermarkets such as Tesco and Sainsbury with 27.5% and 16% respectively. This project was aimed at assessing the salt content in Chinese food, sauces, ingredients, and accompaniments sold in the above supermarkets.

Methodology

Data collection

The chosen method for this study was a systematic sampling of main Chinese food from two outlets, Tesco and Sainsbury. The outlets were chosen based on the number of Chinese cuisines available on their menu. One of the advantages of using systematic sampling is its convenience and the ability to single out samples and access the desired sample size and characteristics (Elfil & Negida, 2017). However, this is limiting as it may not be representative of the entire population. Further, there was a risk of data manipulation which was countered by ensuring the data was collected randomly (Elfil & Negida, 2017)..

A systematic survey was conducted in Tesco and Sainsbury with a primary goal of establishing the mean average sodium concentration in the main Chinese cuisine categories that contribute to salt in the diet bearing in mind most Chinese food uses soy products and other refined oils (Diez-Simon et al., 2020). Data was collected to include mainly Chinese cuisines, however, there was data from Thai and Japanese cuisines that had similar formulations. The data include quality ranges from top middle and bottom, this also included chilled, frozen, and ambient cuisines from across all the categories. For each cuisine, the data also included the weight of the product, price, brand name, serving size, and the amount of salt/100g. Not all products had salt contents, therefore, those that had nil or missing data were rounded up to zero for consistency.

Data analysis

The data was collected and stored in an excel datasheet. It was then imported to the Statistical Package for Social Sciences (SPSS) version 26, where descriptive and inferential statistics were conducted. Out of the 49 observations surveyed, the Chinese ready meal was 82 % followed by the Chinese ready sauces which were 8% of the total product category, and lastly, the Japanese ready sauces and Thai ready meal sauces had 2% each. Descriptive statistics were used to measure the mean value, frequency, standard deviation, and median.

An independent t-test was used to investigate if the mean of the two unrelated groups statistically differed where Salt g/100g was used as the dependent variable and the product subcategory was used as the independent variable. Seven observations were used to conduct the T independent t-test which produced 46 observations as the degrees of freedom. The total number of observations in Tesco was 23 while the total number of observations in Sainsbury’s was 25.

ANOVA test was used to determine the analysis of variance where more Chinese products were selected (89%) as compared to other products from Japan and Thai cuisines. Further, the One-way ANOVA analysis involved three groups that include the complete Chilled meal, complete ambient meal, and complete frozen meal. The product subcategories were used as the independent variable and the Salt g/100g was used as the dependent variable. A subsequent post hoc test was done to detect any significant difference in means between the groups. The average salt content was measured against the FSA 2024 guidelines on sauce-based foods (≤6 g/100 g). (Reference)

Results

Below are the results as analyzed using the SPSS 26 statistical tool. They included descriptive and inferential analysis.

Statistics

Product category

Product sub-category

Outlets

Product Name

Brand name

Brand type

Quality range

N

Valid

49

49

49

49

49

49

49

Missing

0

0

0

0

0

0

0

Table 1.1: frequencies_product category

The total number of valid observations was 49 with 0 missing values for all product categories.

Product category

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

Chinese ready meal

42

85.7

85.7

85.7

Chinese ready sauces

4

8.2

8.2

93.9

Japanese ready sauces

1

2.0

2.0

95.9

Japanese ready meals

2

4.1

4.1

100.0

Total

49

100.0

100.0

Table 1.2: frequencies product subcategory

There were four categories of Chinese cuisine processed foods products (n=4). There were 8.2% (n=4) Chinese ready sauces, 85.7% (n=42) Chinese ready meals, 4.1% (n=2) Japanese ready meal and 2% (n=1) Japanese ready sauces.

Product sub-category

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

chilled meal , complete

27

55.1

55.1

55.1

Ambient meal complete

20

40.8

40.8

95.9

frozen meal complete

2

4.1

4.1

100.0

Total

49

100.0

100.0

Table 1.3: product subcategories

There were three subcategories of the product which included Chilled meal, ambient meal, and frozen meal. There were 55.1% (n=27) Chilled meals, 40.8% (n=20) ambient meals, and 4.1% (n=2) frozen meals.

Brand name

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

1

25

51.0

51.0

51.0

2

24

49.0

49.0

100.0

Total

49

100.0

100.0

Table 1.4: frequencies brand name

There were two brand names included Sainsbury’s and Tesco. There were 25 Sainsbury’s outlets accounting for 51% and 24 Tesco outlets representing the other half.

Quality range

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

Basic

2

4.1

4.1

4.1

Middle

46

93.9

93.9

98.0

Top

1

2.0

2.0

100.0

Total

49

100.0

100.0

Table 1.1: frequencies quality range

Across all products, 4.1% (n=2) were basic range quality, 93.9% (n=46) mid-range quality and 2% (n=1) top range quality product.

Group statistics

Independent sample t Test

Group Statistics

Brand name

N

Mean

Std. Deviation

Std. Error Mean

Salt g/100g

1

23

1.488696

1.9117681

.3986312

2

24

.971563

.9326120

.1903686

Independent Samples Test

Levene’s Test for Equality of Variances

t-test for Equality of Means

F

Sig.

t

df

Sig. (2-tailed)

Mean Difference

Std. Error Difference

95% Confidence Interval of the Difference

Lower

Upper

Salt g/100g

Equal variances assumed

4.027

.051

1.186

45

.242

.5171332

.4358778

-.3607698

1.3950361

Equal variances not assumed

1.171

31.606

.250

.5171332

.4417545

-.3831310

1.4173973

Table 2: independent T test _ product category

The independent T-test indicated a difference in the salt content t (46) =1.253, p=0.043. The salt g/100g did not differ significantly between Tesco branded products (M=1.49, SD=1.91) and Sainsbury’s branded products (M=0.97, SD=0.93).

The p-value is 0.051 which is less than the level of significance thus we fail to reject the null hypothesis and conclude that there is no significant difference in the means of the salt g/100g in the two groups (Tesco branded products and the Sainsbury’s branded products). In the independent T-test table, the mean difference of the salt content g/100g under the equal variances assumed is 0.54 which is not different from the equal variance not assumed.

Table 3: One-way Anova

Descriptive

Salt g/100g

N

Mean

Std. Deviation

Std. Error

95% Confidence Interval for Mean

Minimum

Maximum

Lower Bound

Upper Bound

chilled,meal ,complete

27

.994352

.9232977

.1776887

.629107

1.359596

.0800

4.6000

Ambient meal complete

18

1.645000

2.1124289

.4979043

.594514

2.695486

.2000

8.0000

frozen meal complete

2

.550000

.0707107

.0500000

-.085310

1.185310

.5000

.6000

Total

47

1.224628

1.5003789

.2188528

.784100

1.665155

.0800

8.0000

ANOVA

Salt g/100g

Sum of Squares

df

Mean Square

F

Sig.

Between Groups

5.523

2

2.761

1.239

.299

Within Groups

98.029

44

2.228

Total

103.552

46

Results for One-Way ANOVA for the measure of salt content g/100g

The Chilled meal, ambient meal and frozen meal identified were not significant F (2, 44) = 1.24, p = 0.299. The degree of freedom between the groups is 2, and the degree of freedom within the group is 45. The mean of the Chilled meal is 0.99g and the standard deviation is 0.923. The mean of the ambient meal is 1.65g and the standard deviation is 2.11.

The mean of the frozen meal is 0.55g and the standard deviation is 0.07. The sum of squares between the groups is 5.52 and the sum of squares within the group is 98.03. The p-value is 0.26 which is greater than 0.05 thus we fail to reject the null hypothesis and conclude there is no significant difference in the means of the salt content across the three product subcategories.

Multiple Comparisons

Dependent Variable: Salt g/100g

Tukey HSD

(I) Product sub-category

(J) Product sub-category

Mean Difference (I-J)

Std. Error

Sig.

95% Confidence Interval

Lower Bound

Upper Bound

chilled,meal ,complete

Ambient meal complete

-.6506481

.4541927

.333

-1.752284

.450988

frozen meal complete

.4443519

1.0938409

.913

-2.208740

3.097443

Ambient meal complete

chilled,meal ,complete

.6506481

.4541927

.333

-.450988

1.752284

frozen meal complete

1.0950000

1.1125404

.591

-1.603447

3.793447

frozen meal complete

chilled,meal ,complete

-.4443519

1.0938409

.913

-3.097443

2.208740

Ambient meal complete

-1.0950000

1.1125404

.591

-3.793447

1.603447


A subsequent Tukey post hoc test demonstrated that the subcategories of the products were more likely to have a high salt content in the Ambient meal (M = 1.65, SD = 2.11) than in the chilled meal (M = 0.99, SD = 0.92). However, there were no significant differences in the amount of salt intake in Frozen meals (M = 0.54, SD = 0.06) and either Ambient meals or chilled meals.

Moreover, there is no significant difference between the three subcategories. There is no significant difference in the amount of salt in chilled meals and Ambient meals (p=0.33), there is no difference between the chilled milled and the Frozen meal (p=0.91) and there is no difference between Ambient meals and the Frozen meal (p=0.59).

Table 4:

Salt g/100g

Tukey HSDa,b

Product sub-category

N

Subset for alpha = 0.05

1

frozen meal complete

2

.550000

chilled,meal ,complete

27

.994352

Ambient meal complete

18

1.645000

Sig.

.479

Means for groups in homogeneous subsets are displayed.

a. Uses Harmonic Mean Sample Size = 5.063.

b. The group sizes are unequal. The harmonic mean of the group sizes is used. Type I error levels are not guaranteed.

As represented in the table above, there is one subset. The Ambient meal (M = 1.645), chilled milled (M = 0.994) and frozen meal (M=0.55) fall under one subset. Therefore, the three conditions did not differ from each other.

Figure 1: histogram



Discussion

There were 4 categories of the products, which include the Chinese ready sources, Chinese ready meals, Japanese ready meals, and Japanese ready sources. According to the survey, the Chinese ready meal is the most product category that was sampled. According to the study, the Chinese ready meal was 85.7%, followed by the Chinese ready sauces which were 8.2% of the total product category, 4.1 % of the Japanese ready meals, and 2 % of the Japanese ready sauces.

According to the literature review, Zhang et al. (2020) in research on Chinese processed foods sodium and general safety levels, argues that Chinese processed foods are among the most popular cuisines in the U.K. In addition, the Chinese foods are four-fold saltier and higher in sodium than in the U.K (Zhang et al,2020). Moreover, it explains why Chinese cuisines interest many stakeholders who seek to investigate their salt levels specially to see if they conform to the F.S.A. 2024 standards. Tan et al., (2019) further agree with the above by discussing that Chinese foods have high salt levels with an average of 13 g per day. Additionally, he explains that Chinese products such as sauces account up to 6% of total salt levels. He et al., (2018) in their research reaffirm the above findings through research on Chinese salt and sodium levels research conducted in 2018-2019. In the study findings, the Chinese foods had more salts than the U.K. foods. Specifically, from the researcher’s findings on instant noodles, of 10 sampled, 4 had more salt levels as compared to 2 of the U.K. noodles.

Additionally, 8 out of 11 food groups in China had more salt and sodium content compared to same sampled in the U.K. On average the writer affirms that Chinese products mostly non-processed had 4.5 times more salt than those from U.K. The comparison was done largely on non-processed and large groups of processed foods with little focus on processed foods. Therefore, from the results above, it is true that the Chinese cuisines have more salt content than the Japanese and Thailand meals.

The purpose of the Food standard agencies is to protect public health from risks that may arise in connection with the consumption of food (including risks caused by how it is produced or supplied) and otherwise to protect the interests of consumers concerning food.

Out of the 49 observations surveyed, the Chinese ready meal was 85.7 %.

An independent t test was run where Salt g/100g was used as the dependent variable while product-subcategory was used as the independent variable. $7 observations were used to conduct the T independent t-test which produces 46 observations as the degrees of freedom. The total number of observations in Tesco is 23 while the total number of observations in the Sainsbury’s is 25. The mean of the Tesco is 1.49 with a standard deviation of 1.91, while the mean of is 0.0953 with a mean of 0.953 with a standard deviation of 0.918.

The p-value is 0.051, which is more than the level of significance; thus we fail to reject the null hypothesis and conclude that there is a significant difference in the means of the salt g/100g in the two groups (Tesco and the Sainsbury’s). In the independent T-test table, the mean difference of the salt content g/100g under the equal variances assumed is 0.5171 which is not different from the equal variance not assumed.

One-way Anova was ran. The analysis involved three groups: the Chilled meal complete, ambient meal complete, and frozen meal complete. The product subcategory was used as the independent variable and the Salt g/100g was used as the dependent variable. The degrees of freedom between the groups are 2 and the degrees of freedom within the group is 44. The mean of the Chilled meal complete is 0.994, and the standard deviation is 0.923. the mean of ambient meal complete is 1.645 and the standard deviation is 2.11. the mean of the frozen meal complete is 0.537 and the standard deviation is 0.055. the sum of squares between the group is 6.022 g/100g and the sum of squares within the group is 98.031g/100g. The p-value is 0.299 which is greater than 0.05; thus, we fail to reject the null hypothesis and conclude there is no significant difference in the means of the salt content across the three product subcategories.

The minimum amount of salt content in Chilled meal is 0.08 and the maximum amount of salt content in the chilled meal is 4.6 g/100g. The minimum amount of salt content in Ambient meal is 0.2 g/100g and the maximum amount of salt content in Ambient meal is 8.0 g/100g.

The minimum amount of salt content in Frozen meal is 0.08 g/100g and the maximum amount of salt content in frozen meal is 4.6 g/100g.

According to the subsequent Tukey post hoc test, Ambient meal complete has high salt content with a mean of 1.645g/100g then followed by the chilled milled complete which has a mean of 0.994 g/100g and lastly is the Frozen meal complete that has a mean of 0.54 g/100g

According to the literature review, Antúnez et al. (2019) research on the F.S.A. guidelines and standards on foods’ sodium (salt) content and the anticipated impact explains various measures. Among the main findings is that there are various sub categories of targets to be met by food manufacturers by 2024. For instance, bacon is 1035 sodium (2.59g of salt) per 100 grams of bacon and 430mg sodium (1.08g salt) per 100 grams of sausages. Tan et al. (2019) on research on the same, support the above

Statistics homework help

Sheet1

PM1 OC1 TC1 LE1 PM2 OC2 TC2 LE2
21.7 15.6 17.73 1.78 27 15.79 19.46 2.06
27.8 15.6 17.87 2.25 24.7 13.61 15.98 3.1
24.7 17.2 18.75 1.98 21.8 12.94 15.79 2.68
15.3 8.3 9.21 0.67 23.2 12.97 16.32 2.8
18.4 11.3 12.46 0.86 23.3 11.19 13.49 2.07
14.4 8.4 9.66 1.93 16.2 9.61 12.44 2.14
19 13.2 14.73 1.51 13.4 6.97 8.4 2.32
23.7 11.4 13.23 1.98 13 7.96 10.02 2.18
22.4 13.8 17.08 1.69 16.9 8.43 11.08 2.06
25.6 13.2 15.86 2.3 26.3 14.92 21.46 1.94
15 15.7 17.27 1.24 31.4 17.15 20.57 1.85
17 9.3 10.21 1.44 21.16 15.13 19.64 1.98
23.2 10.5 11.47 1.43 40.1 8.66 11.12 2.66
17.7 14.2 15.64 1.07 28 15.95 19.2 2.32
11.1 11.6 13.48 0.59 4.2 8.91 10.75 2.11
29.8 7 7.795 2.1 15.9 15.19 20.36 2.5
20 19.9 21.2 1.54 20.5 11.73 14.59 2.27
21.6 14.8 15.65 1.73 23.8 14.34 17.64 2.17
14.8 12.6 13.51 1.56 14.6 8.99 11.75 2.74
21 9.1 9.94 1.1 17.8 10.63 13.12 2.45

Statistics homework help

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&DataCopy

&GraphData

&WorkArea

&Miscel_Area

Data

Customer Type of Customer Items Net Sales Method of Payment Gender Marital Status Age
1 Regular 1 39.50 Discover Male Married 32
2 Promotional 1 102.40 Proprietary Card Female Married 36
3 Regular 1 22.50 Proprietary Card Female Married 32
4 Promotional 5 100.40 Proprietary Card Female Married 28
5 Regular 2 54.00 MasterCard Female Married 34
6 Regular 1 44.50 MasterCard Female Married 44
7 Promotional 2 78.00 Proprietary Card Female Married 30
8 Regular 1 22.50 Visa Female Married 40
9 Promotional 2 56.52 Proprietary Card Female Married 46
10 Regular 1 44.50 Proprietary Card Female Married 36
11 Regular 1 29.50 Proprietary Card Female Married 48
12 Promotional 1 31.60 Proprietary Card Female Married 40
13 Promotional 9 160.40 Visa Female Married 40
14 Promotional 2 64.50 Visa Female Married 46
15 Regular 1 49.50 Visa Male Single 24
16 Promotional 2 71.40 Proprietary Card Male Single 36
17 Promotional 3 94.00 Proprietary Card Female Single 22
18 Regular 3 54.50 Discover Female Married 40
19 Promotional 2 38.50 MasterCard Female Married 32
20 Promotional 6 44.80 Proprietary Card Female Married 56
21 Promotional 1 31.60 Proprietary Card Female Single 28
22 Promotional 4 70.82 Proprietary Card Female Married 38
23 Promotional 7 266.00 American Express Female Married 50
24 Regular 2 74.00 Proprietary Card Female Married 42
25 Promotional 2 39.50 Visa Male Married 48
26 Promotional 1 30.02 Proprietary Card Female Married 60
27 Regular 1 44.50 Proprietary Card Female Married 54
28 Promotional 5 192.80 Proprietary Card Female Single 42
29 Promotional 3 71.20 Proprietary Card Female Married 32
30 Promotional 1 18.00 Proprietary Card Female Married 70
31 Promotional 2 63.20 MasterCard Female Married 28
32 Regular 1 75.00 Proprietary Card Female Married 52
33 Promotional 3 63.20 Proprietary Card Female Married 44
34 Regular 1 40.00 Proprietary Card Female Married 34
35 Promotional 5 105.50 MasterCard Female Married 56
36 Regular 1 29.50 MasterCard Male Single 36
37 Regular 2 102.50 Visa Female Single 42
38 Promotional 6 117.50 Proprietary Card Female Married 50
39 Promotional 5 13.23 Proprietary Card Female Married 44
40 Regular 2 52.50 Proprietary Card Female Married 58
41 Promotional 13 198.80 Proprietary Card Female Married 42
42 Promotional 4 19.50 Visa Female Married 46
43 Regular 2 123.50 Proprietary Card Female Married 48
44 Promotional 1 62.40 Proprietary Card Female Married 54
45 Promotional 2 23.80 Proprietary Card Female Married 38
46 Promotional 2 39.60 Proprietary Card Female Married 60
47 Regular 1 25.00 MasterCard Female Married 46
48 Promotional 3 63.64 Proprietary Card Female Married 30
49 Promotional 1 14.82 Proprietary Card Female Married 32
50 Promotional 9 145.20 MasterCard Female Married 46
51 Promotional 6 176.62 Proprietary Card Female Married 38
52 Promotional 5 118.80 Proprietary Card Male Married 68
53 Regular 1 58.00 Discover Female Single 78
54 Regular 2 74.00 Visa Female Single 20
55 Regular 2 49.50 MasterCard Female Married 32
56 Promotional 3 141.60 Proprietary Card Female Married 38
57 Promotional 6 123.10 Proprietary Card Female Married 54
58 Promotional 2 80.40 Proprietary Card Female Married 48
59 Promotional 4 65.20 MasterCard Female Married 46
60 Promotional 4 113.00 Proprietary Card Female Single 50
61 Promotional 1 108.80 Proprietary Card Female Married 46
62 Promotional 3 59.91 Proprietary Card Female Single 30
63 Promotional 5 53.60 Proprietary Card Female Married 54
64 Promotional 1 31.60 Proprietary Card Female Single 42
65 Promotional 2 49.50 Proprietary Card Female Married 48
66 Promotional 1 39.60 Proprietary Card Female Married 62
67 Promotional 2 59.50 Proprietary Card Female Married 34
68 Promotional 5 146.80 Proprietary Card Female Married 28
69 Promotional 2 47.20 Proprietary Card Male Married 46
70 Promotional 8 95.05 Proprietary Card Female Married 54
71 Promotional 5 155.32 Proprietary Card Female Married 30
72 Promotional 4 58.00 MasterCard Female Married 32
73 Regular 1 69.00 Proprietary Card Female Single 22
74 Promotional 2 46.50 Proprietary Card Female Married 32
75 Promotional 2 45.22 Proprietary Card Female Married 74
76 Promotional 4 84.74 Proprietary Card Female Married 62
77 Regular 2 39.00 Proprietary Card Female Married 42
78 Promotional 4 111.14 Proprietary Card Female Married 28
79 Promotional 3 86.80 Proprietary Card Female Married 38
80 Regular 2 89.00 Discover Female Married 54
81 Promotional 2 78.00 MasterCard Female Married 68
82 Promotional 6 53.20 Proprietary Card Female Single 30
83 Promotional 4 58.50 Visa Female Married 36
84 Promotional 3 46.00 Proprietary Card Female Married 44
85 Regular 2 37.50 Visa Female Married 44
86 Promotional 1 20.80 Proprietary Card Female Married 62
87 Regular 6 144.00 MasterCard Female Single 48
88 Regular 4 107.00 Proprietary Card Female Married 36
89 Promotional 1 31.60 Proprietary Card Female Single 20
90 Promotional 6 57.60 Proprietary Card Female Married 42
91 Promotional 4 95.20 Proprietary Card Female Married 54
92 Promotional 1 22.42 Proprietary Card Female Married 54
93 Regular 5 159.75 Proprietary Card Female Married 72
94 Promotional 17 229.50 Proprietary Card Female Married 30
95 Regular 3 66.00 American Express Female Married 46
96 Regular 1 39.50 MasterCard Female Married 44
97 Promotional 9 253.00 Proprietary Card Female Married 30
98 Promotional 10 287.59 Proprietary Card Female Married 52
99 Promotional 2 47.60 Proprietary Card Female Married 30
100 Promotional 1 28.44 Proprietary Card Female Married 44

Statistics homework help

Data

Colleges and Universities Normalized Data Distance Matrix (first five)
School Type Median SAT Acceptance Rate Expenditures/Student Top 10% HS Graduation % School Type Median SAT Acceptance Rate (%) Expenditures/Student Top 10% HS Graduation % Amherst Barnard Bates Berkeley Bowdoin
Amherst Lib Arts 1315 22% $26,636.00 85 93 Amherst Lib Arts 0.8280 -1.2042 -0.2214 0.7967 1.3097 Amherst 0 3.528429241 2.7006876027 4.2454058294 0.7157907639
Barnard Lib Arts 1220 53% $17,653.00 69 80 Barnard Lib Arts -0.6877 1.1141 -0.8024 -0.3840 -0.4356 Barnard 0 1.8790140078 2.8901006639 2.9744381066
Bates Lib Arts 1240 36% $17,554.00 58 88 Bates Lib Arts -0.3686 -0.1572 -0.8088 -1.1958 0.6384 Bates 0 3.9836721315 2.061542031
Berkeley University 1176 37% $23,665.00 95 68 Berkeley University -1.3897 -0.0824 -0.4136 1.5347 -2.0467 Berkeley 0 3.8954242852
Bowdoin Lib Arts 1300 24% $25,703.00 78 90 Bowdoin Lib Arts 0.5887 -1.0546 -0.2818 0.2801 0.9069 Bowdoin 0
Brown University 1281 24% $24,201.00 80 90 Brown University 0.2856 -1.0546 -0.3789 0.4277 0.9069
Bryn Mawr Lib Arts 1255 56% $18,847.00 70 84 Bryn Mawr Lib Arts -0.1293 1.3385 -0.7252 -0.3102 0.1014
Cal Tech University 1400 31% $102,262.00 98 75 Cal Tech University 2.1842 -0.5311 4.6692 1.7561 -1.1069
Carleton Lib Arts 1300 40% $15,904.00 75 80 Carleton Lib Arts 0.5887 0.1419 -0.9155 0.0587 -0.4356
Carnegie Mellon University 1225 64% $33,607.00 52 77 Carnegie Mellon University -0.6079 1.9368 0.2294 -1.6386 -0.8384
Claremont McKenna Lib Arts 1260 36% $20,377.00 68 74 Claremont McKenna Lib Arts -0.0495 -0.1572 -0.6262 -0.4578 -1.2412
Colby Lib Arts 1200 46% $18,872.00 52 84 Colby Lib Arts -1.0068 0.5906 -0.7235 -1.6386 0.1014
Colgate Lib Arts 1258 38% $17,520.00 61 85 Colgate Lib Arts -0.0814 -0.0076 -0.8110 -0.9744 0.2356
Columbia University 1268 29% $45,879.00 78 90 Columbia University 0.0781 -0.6807 1.0230 0.2801 0.9069
Cornell University 1280 30% $37,137.00 85 83 Cornell University 0.2696 -0.6059 0.4576 0.7967 -0.0329
Davisdson Lib Arts 1230 36% $17,721.00 77 89 Davisdson Lib Arts -0.5281 -0.1572 -0.7980 0.2063 0.7727
Duke University 1310 25% $39,504.00 91 91 Duke University 0.7483 -0.9798 0.6107 1.2395 1.0412
Georgetown University 1278 24% $23,115.00 79 89 Georgetown University 0.2377 -1.0546 -0.4491 0.3539 0.7727
Grinnell Lib Arts 1244 67% $22,301.00 65 73 Grinnell Lib Arts -0.3048 2.1611 -0.5018 -0.6792 -1.3754
Hamilton Lib Arts 1215 38% $20,722.00 51 85 Hamilton Lib Arts -0.7675 -0.0076 -0.6039 -1.7124 0.2356
Harvard University 1370 18% $46,918.00 90 90 Harvard University 1.7056 -1.5033 1.0902 1.1657 0.9069
Haverford Lib Arts 1285 35% $19,418.00 71 87 Haverford Lib Arts 0.3494 -0.2320 -0.6882 -0.2364 0.5041
Johns Hopkins University 1290 48% $45,460.00 69 86 Johns Hopkins University 0.4292 0.7402 0.9959 -0.3840 0.3699
Middlebury Lib Arts 1255 25% $24,718.00 65 92 Middlebury Lib Arts -0.1293 -0.9798 -0.3455 -0.6792 1.1754
MIT University 1357 30% $56,766.00 95 86 MIT University 1.4981 -0.6059 1.7270 1.5347 0.3699
Mount Holyoke Lib Arts 1200 61% $23,358.00 47 83 Mount Holyoke Lib Arts -1.0068 1.7124 -0.4334 -2.0076 -0.0329
Northwestern University 1230 47% $28,851.00 77 82 Northwestern University -0.5281 0.6654 -0.0782 0.2063 -0.1671
Oberlin Lib Arts 1247 54% $23,591.00 64 77 Oberlin Lib Arts -0.2569 1.1889 -0.4184 -0.7530 -0.8384
Occidental Lib Arts 1170 49% $20,192.00 54 72 Occidental Lib Arts -1.4854 0.8150 -0.6382 -1.4910 -1.5097
Pomona Lib Arts 1320 33% $26,668.00 79 80 Pomona Lib Arts 0.9078 -0.3816 -0.2194 0.3539 -0.4356
Princeton University 1340 17% $48,123.00 89 93 Princeton University 1.2269 -1.5781 1.1681 1.0919 1.3097
Rice University 1327 24% $26,730.00 85 88 Rice University 1.0195 -1.0546 -0.2154 0.7967 0.6384
Smith Lib Arts 1195 57% $25,271.00 65 87 Smith Lib Arts -1.0866 1.4133 -0.3097 -0.6792 0.5041
Stanford University 1370 18% $61,921.00 92 88 Stanford University 1.7056 -1.5033 2.0604 1.3133 0.6384
Swarthnore Lib Arts 1310 24% $27,487.00 78 88 Swarthnore Lib Arts 0.7483 -1.0546 -0.1664 0.2801 0.6384
U Michigan University 1195 60% $21,853.00 71 77 U Michigan University -1.0866 1.6376 -0.5308 -0.2364 -0.8384
U of Chicago University 1300 45% $38,937.00 74 73 U of Chicago University 0.5887 0.5159 0.5740 -0.0151 -1.3754
U of Rochester University 1155 56% $38,597.00 52 73 U of Rochester University -1.7248 1.3385 0.5521 -1.6386 -1.3754
U Pennsylvania University 1280 41% $30,882.00 87 86 U Pennsylvania University 0.2696 0.2167 0.0531 0.9443 0.3699
U Va University 1218 37% $19,365.00 77 88 U Va University -0.7196 -0.0824 -0.6917 0.2063 0.6384
UCLA University 1142 43% $26,859.00 96 61 UCLA University -1.9322 0.3663 -0.2070 1.6085 -2.9865
UNC University 1109 32% $19,684.00 82 73 UNC University -2.4587 -0.4563 -0.6710 0.5753 -1.3754
Vassar Lib Arts 1287 43% $20,179.00 53 84 Vassar Lib Arts 0.3813 0.3663 -0.6390 -1.5648 0.1014
Washington U (MO) University 1225 54% $39,883.00 71 76 Washington U (MO) University -0.6079 1.1889 0.6352 -0.2364 -0.9727
Washinton and Lee Lib Arts 1234 29% $17,998.00 61 78 Washinton and Lee Lib Arts -0.4643 -0.6807 -0.7801 -0.9744 -0.7042
Wellesley Lib Arts 1250 49% $27,879.00 76 86 Wellesley Lib Arts -0.2090 0.8150 -0.1411 0.1325 0.3699
Wesleyan (CT) Lib Arts 1290 35% $19,948.00 73 91 Wesleyan (CT) Lib Arts 0.4292 -0.2320 -0.6540 -0.0889 1.0412
Williams Lib Arts 1336 28% $23,772.00 86 93 Williams Lib Arts 1.1631 -0.7555 -0.4067 0.8705 1.3097
Yale University 1350 19% $52,468.00 90 93 Yale University 1.3865 -1.4285 1.4491 1.1657 1.3097
Mean 1263.10 0.38 30060.33 74.20 83.24
Std Dev 62.68 0.13 15463.31 13.55 7.45

Statistics homework help

Data

Background Ariel Calibri Tahoma
white background 301 225 217
white background 288 250 259
white background 234 173 234
white background 381 267 270
white background 295 356 245
white background 351 253 239
white background 298 230 268
white background 290 261 245
white background 311 294 273
white background 355 216 265
green background 275 258 261
green background 271 216 193
green background 210 203 280
green background 324 223 282
green background 327 159 227
green background 200 178 217
green background 257 241 180
green background 266 312 285
green background 205 310 254
green background 194 310 313
pink background 209 251 201
pink background 292 273 247
pink background 261 269 188
pink background 247 121 198
pink background 259 344 221
pink background 284 224 204
pink background 161 181 208
pink background 291 252 256
pink background 205 181 174
pink background 323 253 167

Statistics homework help

RESEARCH ARTICLE Open Access

General self-efficacy modifies the effect of
stress on burnout in nurses with different
personality types
Yongcheng Yao1,2* , Shan Zhao1, Xia Gao1, Zhen An1, Shouying Wang1, Hongbin Li1, Yuchun Li1, Liyun Gao1,
Lingeng Lu3 and Ziming Dong2

Abstract

Background: Burnout is a health problem in nurses. Individuals with a certain personality are more susceptible to
job-related burnout. General self-efficacy (GSE) is an important predictor of job-related burnout. The relationships
between general self-efficacy, job-related burnout and different personality types are still not clear. This study aims
to analyze the relationships of job-related burnout, stress, general self-efficacy and personality types, as well as their
interactions in job-related burnout.

Method: A cross-sectional survey of 860 nurses was conducted between June and July 2015 in China. We measured
their job-related burnout using the scale of the Maslach Occupational Burnout Scale, and personality, stress, and GSE.
Machine learning of generalized linear model were performed.

Results: Maslach Burnout Inventory (MBI) professional efficacy was significantly associated with gender, marital status,
age, job title and length of service. A machine learning algorithm showed that stress was the most important factor in
job-related burnout, followed by GSE, personality type (introvert unstable), and job title. Individuals with low GSE and
either introversion or unstable (high neuroticism) personality seemed to have stronger burnout when they faced stress
(regardless of stress intensity) compared to others.

Conclusion: Stress, GSE and introvert unstable personality are the top three factors of job-related burnout. GSE
moderates the effect of stress on burnout in nurses with extroversion or neuroticism personality. Reducing
stress, increasing GSE, and more social support may alleviate job-related burnout in nurses. Nurses with introvert unstable
personality should be given more social support in reducing stress and enhancing their GSE.

Keywords: Nurse, Job-related burnout, Personality, General self-efficacy, Machine learning, Interaction

Background
Burnout is characteristic of depersonalization, emotional
exhaustion and low personal accomplishment [1]. Job-
related burnout in health care sector not only leads to
decreased effectiveness at work, but may also interfere
human perception, affecting an individual’s appropriate
judgement, reducing the ability to predict accidents,
consequently leading to the illegal operations and even
the occurrence of medical accidents, deteriorating the

quality of care provided to patients [2, 3]. Burnout
frequently occurs in people-oriented profession, and es-
pecially medical staffs, who provide care services for pa-
tients and face more challenges such as the demanding
relationships with patients and their relatives, interac-
tions with coworkers in teams, are more susceptible to
job-related burnout [4]. A survey of medical staffs
showed that more than one-third of the participants
(35.8%) reported themselves at the high risk of job-re-
lated burnout, 27.2% had a high degree of exhaustion,
10.0% had a certain degree of cynicism, 3.2% lacked pro-
fessional efficacy [5]. Another survey of 218 medical
staffs showed that 42.1% of the subjects had a certain de-
gree of exhaustion, 22.7% had a certain degree of

* Correspondence: yaoyongchengbb@126.com
1School of Public Health, Xinxiang Medical University, Xinxiang 453003,
Henan, China
2School of Basic Medical Sciences, Zhengzhou University, Zhengzhou 450001,
Henan, China
Full list of author information is available at the end of the article

© The Author(s). 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0
International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and
reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to
the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver
(http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

Yao et al. BMC Health Services Research (2018) 18:667
https://doi.org/10.1186/s12913-018-3478-y

cynicism, 48.6% lacked professional efficacy [6]. One re-
cent study shows over half of nurses working in Vet-
erans Health Administration (VHA) of the Department
of Veterans Affairs suffer emotional exhaustion and/or
low accomplishment and/or high depersonalization [7].
Margues and colleagues reported that there were 59%
and 41% nurses with high level of emotional exhaustion
and lack of personal accomplishment, respectively, in a
University hospital of Portugal [8]. The prevalence of
burnout was 12% in pediatric palliative care provider in
the United States [9], whereas its prevalence was rela-
tively high in mental healthy, ranging from 21 to 67%
[10–12].
Personality is a sum of psychological characteristics in

a relatively stable individual, reflecting one’s adaptability
to the environment based on the unique behavior pat-
terns and ways of thinking, and is a product of the inter-
action with the acquired social environment on the basis
of natural qualities. The involvement of personality has
been reported in the development of burnout, and some
individuals with a certain personality trait are more sus-
ceptible to job-related burnout [13, 14]. General charac-
ters for the vulnerable individuals include unrealistic
ideals and expectations, low self-worth and judgment,
lack of self-confidence, lack of accurate understanding of
their advantages and limitations [15, 16]. In contrast,
those with active coping strategies and the sense of
self-efficacy are relatively more immune to burnout [17,
18]. Individuals with a stable extrovert personality have a
strong motivation in their actions, while those having
cynicism and extroversion appear at the risk of burnout
and other mental illnesses [19, 20] . Studies have shown
that medical staffs have a stronger emotional response
and stubborn behavior compared to the general popula-
tion [21]. Furthermore, personality types are associated
with the sub-dimensions of job-related burnout; exhaus-
tion and cynicism more frequently occur in individuals
with the type A personality. Emotional stability is nega-
tively correlated with psychological fatigue, depression,
and irritability [22]. A meta-analysis shows that Type A
personality was linked to personal accomplishment [23].
General self-efficacy (GSE) refers to an overall self-

confidence that an individual responds to different envir-
onmental challenges or face new things. It predicts an
individual’s behavior, thinking, and emotional reactions.
Studies shows that GSE has a significant direct and in-
direct association with mental health such as depression,
anxiety and helplessness [1]. Another study shows that
both GSE and professional efficacy are in significantly
negative correlation with exhaustion, suggesting that
GSE is an important predictor of job-related burnout
[24]. Individuals with low GSE also have low self-esteem
and pessimistic thoughts of their accomplishments. Job-
related burnout can, in turn, reduce self-efficacy, leading

to depression, irritability, helplessness, anxiety and other
negative emotions [25, 26]. An inverse correlation was
found between the self-efficacy and each of the three di-
mensions of burnout in nurses [27]. Therefore, GSE is
an important factor in relation to burnout.
In the previous study, we found that high GSE could

not only significantly ameliorate stress but also improve
job-satisfaction in nurses [28], both of which are related
to burnout and personality. However, it is still unclear
how GSE, job-related burnout and different personality
types are related to each other in nurses. Burnout is a crit-
ical and well-studied outcome of job-stress [29]. High self-
efficacy and optimistic personality may protect nurses
from the negative effect of job-stress [23, 30]. Thus, stress,
GSE and personality may orchestrate together in job-re-
lated burnout. Thus, the purposes of this cross-sectional
study aimed to investigate the relationships between
job-related burnout, stress, GSE and personality type, as
well as their interactions in job-related burnout in nurses
in China.

Methods
Participants
The protocol of this study was approved by the ethics
committee of Xinxiang Medical University. This study
was conducted through a convenience sample of regis-
tered nurses from five municipal hospitals in Henan
Province, China. The criteria for the inclusion are those
who are registered nurses and have worked in a nurse
position for at least 1 year. Based on the criteria, 1100
registered nurses were identified eligible through the hu-
man resource department of the hospitals. Of them, 860
agreed to participate when they were informed about the
purposes of this study, and successfully completed the
survey. The participation rate was 78.2%.

Study instruments
Socio-demographic characteristics
A questionnaire (Additional file 1) was handed to the
participants in the hospitals for the collection of selected
socio-demographic characteristics including gender, age,
professional experience, marital status, hospital depart-
ment, and job title.

Maslach burnout inventory – general survey
Burnout syndrome was assessed using the Maslach
Burnout Inventory-General Survey (MBI-GS) [31],
which was previously translated into Chinese with a
good reliability and validity in a Chinese sample [32,
33]. The MBI-GS consists of three dimensions with a
total of 15 items rating on a Likert scale from 0 to 6
points: exhaustion (EX, five items), cynicism (CY, four
items), and professional efficacy (PE, six items). The
score of each dimension is the sum of the items in that

Yao et al. BMC Health Services Research (2018) 18:667 Page 2 of 9

dimension. The level of burnout is positively related to
the score. Since PE is scored in an opposite direction,
the level of professional efficacy is negatively related to
PE score. The Cronbach’s Alpha of the scale in this
study was 0.850.
The cutoff points were taken to evaluate job-related

burnout based on the criteria used by Li Yongxin with
minor modification [34]. The cutoff point of upper one
two-third of each dimension of the survey sample was
used for job-related burnout (EX of 14, CX of 7, PE of
14). The burnout degree of the survey sample was di-
vided into the following four levels: Zero burnout (all
three dimensions scoring below the cutoff points); Mild
burnout (any one dimension scoring above the cutoff
point); Moderate burnout (any 2 dimensions scoring
above the cutoff points), and Severe burnout (all three
dimensions scoring above the cutoff points).

Measurement of general self-efficacy
The Schwazer’s GSE Scale (Chinese version) was applied
to measure GSE [35]. It consists of 10 items on a 4-point
rating scale. Higher scores suggest higher levels of GSE.
Homogeneity reliability scored 0.883 in this study.

Measurement of stress
We adopted the Occupational Stress Inventory-Revised
(OSI-R) [36] to assess the levels of stress, which consists
of 20 items, 10 each for psychological and physical
stress. Each item scales 5 points. The sum score was cal-
culated for psychological and physical stress, respect-
ively. A high score indicates a high level of the stress. Its
consistency reliability in this study was 0.881.

Measurement of personality type
Personality was assessed using two scales of the simpli-
fied Chinese version of Eysenck’s Personality
Questionnaire-Revised (EPQ-RSC) [37] provides an ex-
cellent instrument for personality research, which in-
cludes 24 items with each scoring either 0 or 1. The
neuroticism scale (EPQ-N), which assesses emotional
stability while the extroversion scale (EPQ-E) assesses
the need for emotional stimulation. Each scale was di-
vided into high and low categories based on the me-
dians as the cutoff points as reported in literature, an
accepted method in analyzing the psychometric scale
[38]. A high score was defined as an EPQ-E C60 and an
EPQ-N C61 [39], and based on which four types of per-
sonality were classified: introvert stable (low EPQ-E, low
EPQ-N), extrovert stable (high EPQ-E, low EPQ-N),
extrovert unstable (high EPQ-E, high EPQ-N) and intro-
vert unstable (low EPQ-E, high EPQ-N).

Data analysis
Data were recorded and analyzed using Epidata3.1 and
SPSS (version 15 for Windows). Numerical variables
are presented as mean ± standard deviation (SD). A
two-tailed test yielding p < 0.05 was considered statisti-
cally significant. Either t-test or Analysis of Variance
(ANOVA) was used to analyze the differences between
the groups, and post hoc Bonferroni tests were per-
formed to verify the differences between the specific
groups in analyzing associations of demographic variables
with job-related burnout syndrome components, and gen-
eral self-efficacy. Machine learning of generalized linear al-
gorithm (GLM) using H2O.ai (http://docs.h2o.ai/h2o/
latest-stable/h2o-docs/flow.html) was performed to analyze
the importance of the factors in job-related burnout, in
which the subjects were randomly (ratio = 0.70) divided
into training and validation datasets [40]. GLM was fitted
to estimate the set of parameters by maximizing the log-
likelihood of the data for the best model. A Gaussian family
and 10-fold cross-validation were set, and the default was
set for other parameters in the modeling. ModGraph [41]
was used to construct graphs for the interactions between
GSE, stress and personality in job-related burnout after
multivariate regression analyses for their interactions fol-
lowing the recommendation by Dawson and Richter [42] to
analyze the 3-way interactions in either neuroticism or
extroversion personality, respectively, to increase the ana-
lysis power by keeping the number of participants not too
small in each subgroup.

Results
The prevalence of job-related burnout in nurses
Of all the 860 nurses who agreed to participate and suc-
cessfully completed the survey, 68.1% (n = 586) of the
participants had job-related burnout. Of 586 nurses, 279
(32.4%) were mild job-related burnout, 238 (27.7%) were
moderate job-related burnout, 69 (8.0%) were severe
job-related burnout.

Associations of demographic variables and personality
types with burnout syndrome components, and general
self-efficacy of nurses
Association analytic results are shown in Table 1. There
was statistically significant association between gender
and MBI-GS (p < 0.05) with males having higher job-re-
lated burnout than females. Male nurses showed signifi-
cantly higher professional efficacy than female ones (P
< 0.01). There was significantly higher MBI-GS profes-
sional efficacy in single nurses compared with married
nurses (P < 0.05). Professional efficacy (PE) reduced grad-
ually with both age and the length of service in years (P <
0.01). Post hoc test results showed that nurses ageing 30~
years or with 1~ years of service scored significantly
higher on the professional efficacy subscale than nurses

Yao et al. BMC Health Services Research (2018) 18:667 Page 3 of 9

40~ years or with 20~ years, respectively. There was a sig-
nificant association between the exhaustion scores and de-
partment (P < 0.05); the nurses in emergency departments
scored significantly higher on the exhaustion subscale
than nurses in Obstetrics and gynecology and other

departments. Nurses with a primary title had significantly
higher professional efficacy scores than those with an
intermediate title (P < 0.05).
There was no significant relationships between either

the gender or marital status and GSE (p > 0.05). GSE

Table 1 Associations of Demographic variables with job-related burnout syndrome components, and General Self-efficacy in nurses
(mean ± SD)

Variable N MBI-GS MBI-GS: EX MBI-GS: CY MBI-GS: PE GSE

Gender

Male 48 35.2 ± 13.5 11.9 ± 6.9 8.4 ± 6.2 14.9 ± 8.1 24.9 ± 5.4

Female 812 30.9 ± 14.1 13.2 ± 6.7 7.0 ± 5.4 10.7 ± 8.8 25.5 ± 5.6

t 2.057* −1.268 1.682 3.241** −0.688

Marital status

Single 448 31.4 ± 14.2 12.7 ± 6.6 7.1 ± 5.4 11.6 ± 8.5 25.3 ± 5.5

Married 412 30.8 ± 14.0 13.5 ± 6.8 7.1 ± 5.5 10.2 ± 9.0 25.6 ± 5.7

t 0.678 −1.820 0.096 2.424* −0.749

Age

< 30 622 31.4 ± 13.7 12.8 ± 6.6 7.0 ± 5.3 11.5 ± 8.7 25.2 ± 5.4

30~ 168 31.7 ± 15.6 14.2 ± 7.0 7.6 ± 5.9 10.0 ± 8.7 25.5 ± 6.2

40~ 70 27.5 ± 13.3 12.8 ± 6.7 6.4 ± 5.8 8.3 ± 9.3 27.5 ± 5.3

F 2.616 2.649 1.362 5.484** 5.427**

Length of service (yrs)

1~ 666 31.4 ± 13.9 12.8 ± 6.6 7.0 ± 5.3 11.5 ± 8.7 25.2 ± 5.5

10~ 116 31.7 ± 15.8 14.5 ± 7.0 7.8 ± 6.0 9.3 ± 8.3 25.6 ± 5.8

20~ 78 28.0 ± 13.2 13.2 ± 6.9 6.5 ± 5.9 8.4 ± 9.1 27.0 ± 6.1

F 2.078 2.921 1.675 6.855** 3.621*

Department

Emergency 114 34.7 ± 14.0 15.1 ± 7.1 8.0 ± 5.3 11.6 ± 8.3 24.9 ± 5.5

Surgical 145 31.5 ± 14.9 13.6 ± 6.9 7.6 ± 5.6 10.3 ± 8.4 25.0 ± 5.4

Pediatric 44 32.8 ± 15.5 14.8 ± 7.9 7.0 ± 6.1 11.0 ± 9.7 25.9 ± 6.1

Obstetrics and gynecology 95 29.9 ± 13.2 12.0 ± 5.9 7.0 ± 4.7 10.9 ± 8.9 26.1 ± 6.2

Medicine 186 29.7 ± 13.9 13.1 ± 6.9 6.4 ± 5.4 10.3 ± 8.7 25.3 ± 5.4

Mental Health 100 33.2 ± 13.1 12.4 ± 6.6 8.0 ± 5.7 12.8 ± 9.1 24.9 ± 5.7

Other 176 29.0 ± 13.8 12.0 ± 6.0 6.3 ± 5.3 10.7 ± 9.0 25.9 ± 5.6

F 2.810* 3.764** 2.198* 1.224 1.029

Job title

Primary 718 31.3 ± 14.1 13.0 ± 6.7 7.0 ± 5.3 11.2 ± 8.7 25.1 ± 5.5

Intermediate 142 30.4 ± 14.2 13.5 ± 7.0 7.4 ± 6.0 9.5 ± 8.9 26.8 ± 6.0

t 0.707 −0.827 −0.596 2.173* −3.260**

Personality type

Introvert Stable 170 28.3 ± 13.0 11.6 ± 6.3 5.7 ± 4.3 10.9 ± 9.2 25.8 ± 5.2

Extrovert Stable 223 24.9 ± 12.7 10.7 ± 5.9 5.2 ± 5.1 8.9 ± 8.2 27.6 ± 5.4

Introvert Unstable 283 36.2 ± 14.1 15.0 ± 6.7 9.0 ± 5.8 12.2 ± 8.6 23.3 ± 5.0

Extrovert Unstable 184 33.5 ± 13.2 14.4 ± 6.8 7.5 ± 5.2 11.6 ± 8.9 25.7 ± 5.9

F 34.29*** 23.07*** 26.80*** 6.38*** 27.93***

Note: *P < 0.05, **P < 0.01, ***P < 0.001. MBI-GS Maslach burnout inventory-general survey, EX Exhaustion, CY Cynicism, PE Professional efficacy, GSE
General self-efficacy

Yao et al. BMC Health Services Research (2018) 18:667 Page 4 of 9

increased gradually with either age or the length of ser-
vice increasing. Post hoc test results showed that nurses
ageing 40~ years scored significantly higher on the GSE
subscale than other age groups (P < 0.05), and nurses
with 20~ years of service scored significantly higher on
the GSE subscale than nurses with 1~ years (P < 0.05).
Nurses with an intermediate titles had significantly
higher GSE scores than those with a primary title (entry
level) (P < 0.01). There was no significant relationship
between different departments and GSE (p > 0.05).
Differences in all dimensions of job-related burnout

and GSE were statistically significant in the four person-
ality types (P < 0.001) (Table 1) Post hoc test results
showed that stable nurses scored significantly lower on
MBI-GS and the exhaustion subscale than unstable ones
(P < 0.01). Extrovert stable nurses scored significantly
lower professional efficacy than unstable one (P < 0.05).

Importance of risk factors in job-related burnout
Several risk factors of burnout, such as gender, age,
marital status, work shift and personality, have been
identified in nurses [43, 44]. However, the relative im-
portance of these factors in burnout has not been re-
ported. To explore the importance of the risk factors in
job-related burnout, we performed H2O’s machine
learning (H2OFlow of H2O.ai) of generalized linear
model algorithm, and the results are shown in Fig. 1
(blue stands for a positive association, and orange for a
negative one). Stress ranked no. 1 (standardized coeffi-
cient = 4.89) in the risk factors of job-related burnout,
followed by GSE (standardized coefficient = − 3.39),
introvert unstable personality, job title, extrovert and
introvert stable personality, age, marital status, extrovert
unstable personality, gender and length of service. The
risk factors of stress, introvert and extrovert unstable
personality, job title, and length of service showed posi-
tive correlations with job-related burnout. In contrast,

GSE, extrovert and introvert stable personality, age,
marital status and gender (women) had negative correl-
ation with job-related burnout.

Joint effect of GSE, burnout and personality types on
stress
Table 2 shows the correlations between variables. There
was a significantly positive and moderate correlation
between burnout and stresses and Extroversion (r =
0.44, 0.35 respectively, p < 0.01). Burnout was signifi-
cantly negatively correlated with GSE and Neuroticism
(r = − 0.39, 0.23 respectively, p < 0.01).
Table 3 shows the results of three different multivari-

ate models. In the model 1, as expected, stress, and
GSE but extroversion personality showed significant as-
sociations with burnout, with stress having a positive
association and GSE having a negative association. In
the model 2 of the 2-way interactions, there was a sig-
nificant interaction between stress and extroversion,
but neither between GSE and extroversion, nor be-
tween GSE and stress. However, in the model 3 of the
3-way interactions, the interaction of stress, GSE and
extroversion was significant (p = 0.039), whereas the
significance of main effect of stress was not held, and
GSE still remained significant.
To visualize the effect of stress, GSE and extroversion

in burnout, we further constructed the graph based on

Fig. 1 The variable importance in job-related burnout. The factors are ranked based on their importance in burnout. The blue bar stands for the
factor having a positive coefficient with burnout, while the orange bar stands for the factor having a negative coefficient with burnout

Table 2 Pearson Correlations of the variables (n = 847)

Variable M SD Burnout GSE Stress Extroversion

Burnout 30.8 13.8 1.00

GSE 25.4 5.5 −0.38** 1.00

Stress 52.7 11.6 0.43** −0.29** 1.00

Extroversion 7.1 2.7 −0.23** 0.27** −0.31** 1.00

Neuroticism 5.9 3.0 0.35** −0.28** 0.50** −0.25**

Note: *p < 0.05, **p < 0.01. GSE General self-efficacy

Yao et al. BMC Health Services Research (2018) 18:667 Page 5 of 9

the method as described by Dawson and Richter [42]
(Fig. 2). Individuals with low GSE and low extroversion
seemed to have stronger burnout when they experi-
enced stress (regardless of stress intensity) compared to
others. The introvert individuals had an overall higher
burnout than those extrovert regardless of the GSE.
Similarly, we examined the interaction of stress, GSE

and neuroticism personality in burnout (Table 4). In the
model 3, we found there was a significant 3-way inter-
action of stress, GSE and neuroticism personality (p =
0.045). Figure 3 shows that individuals with low GSE
and unstable (high neuroticism) seemed to have stronger
burnout when they faced stress (regardless of stress in-
tensity) compared to others, while those with high GSE
and unstable had the lowest burnout.

Discussion
This study showed that the prevalence of job-related
burnout in Chinese nurses was 68.1%, and was higher
than that reported by Wang [45, 46]. The prevalence of
job-related burnout in female was lower than male, and
was the highest in nurses who are married, or over

30 years old age, or had over 10 years length of service,
or worked in surgical department. This finding is in
consistence with the results of our previous studies
[44]. This finding also suggests that the job-related
burnout in Chinese nurses is a big health problem and
should not be ignored. Nurses often directly interact
with patients and their families, requiring not only
strong medical skills, but also the strong interpersonal
relationship skills. Relatively severe pressure and the
often duty-shift for nurses make them susceptible to
job-related burnout.
Influenced by Chinese traditional culture, women

nurses are still predominant in Chinese hospitals, and a
very few men would like to take nursing job as their pro-
fessional career until today. Thus, the lack of the recog-
nition of the nurse profession may be one of the reasons
for the sense of low accomplishment in male nurses.
Similarly, the sense of low achievement was also ob-
served in younger and unmarried nurses. This finding is
consistent with the results of other previous studies [47,
48]. Maslach et al. reported that the levels of job-related
burnout in young employees was relatively high [29] .
One possibility for young employees is due to the short
service, heavy community pressure, poor job adaptabil-
ity, and the lack of autonomy. With age increasing and
job status rising, the job initiative and accomplishment
were much stronger and consequently, job-related burn-
out reduced gradually.
Emergency department is often on duty 24 h a day

and 7 days a week to face emergencies and deal with
critical patients. In addition, task of nurses in emergency
department is heavy with great responsibility, and they
are always in highly tense condition. Thus, the job-re-
lated burnout in this group is prominent. However, this
hospital department-based analysis may not reflect the
staff shortages or the volume of patients nurses cared
for. Thus, further analyses with the adjustment of the
volume of patients and the number of nurses in each
department could be performed in the future research.

Table 3 Effects of GSE, extroversion and stress on burnout in
multivariate regression analyses

Variable Model 1 Model 2 Model 3

β p value β P value β P value

stress 0.403 < 0.001 0.391 0.039 −0.493 > 0.05

GSE −0.669 < 0.001 −1.21 0.01 −3.124 0.003

E −0.25 > 0.05 1.707 > 0.05 −4.988 > 0.05

stress×GSE 0.011 > 0.05 0.046 0.013

stress×E −0.037 0.005 0.089 > 0.05

GSE × E 0 > 0.05 0.261 0.044

stress×GSE × E −0.005 0.039

Adjusted R2 0.256 0.261 0.264

ΔR2 0.258 < 0.001 0.008 < 0.05 0.004 0.039

β: standardized coefficient; GSE General self-efficacy, E Extroversion

Fig. 2 Interaction of GSE, stress, extroversion personality on burnout in nurses

Yao et al. BMC Health Services Research (2018) 18:667 Page 6 of 9

Self-efficacy refers to the belief that an individual has
an ability to take action and achieve a given goal [49].
GSE has nothing to do with the actual skills of individ-
uals, but is related to the self-judgment for the individ-
uals’ decision to apply their skills. It has been reported
that individuals with high self-efficacy tend to adopt
positive coping strategies when they face with severe
pressure, believing that they are able to complete the
tasks and do not feel too much pressure [50]. Studies
have shown that personality type is an important factor
in job-related burnout, and individuals with a certain
personality type tend to be susceptible to job-related
burnout [51]. In our study, the interactions between
GSE, stress and extroversion or neuroticism showed
that Extrovert nurses with better GSE had less burnout,
and unstable ones with low GSE had relatively stronger
burnout when they faced job challenges or stress. In
the nurses with extroversion but not neuroticism per-
sonality, GSE could completely moderate the effect of
stress on burnout. Generally, response of emotionally
stable nurses to job stress is gentle, and they are quickly
calmed down when they face the provocation of the pa-
tients or their family members. However, emotional

unstable individuals are impulsive, irritable and sensi-
tive, particularly if their GSE are also relatively low,
their feelings of burnout are stronger. Thus, this finding
suggests that appropriate measures may reduce the ef-
fect of stress on burnout based on the personality type
of extroversion or neuroticism.
A variety of factors influence job-related burnout. We

found that stress is the most important risk factor in
job-related burnout, whereas GSE is the most import-
ant protective factor. Different personalities had differ-
ent associations with job-related burnout; introvert
unstable is a risk factor, whereas extrovert stable pro-
tects individuals from job-related burnout. Due to the
limitation of time and data, the study participants en-
rolled in this study were mainly from the municipal
hospitals with relatively heavy patient loads, and may
have selection bias leading to overestimate the preva-
lence of burnout. However, this is a real situation in
China, more patients particularly with relatively com-
plicated or severe diseases directly see doctors in a mu-
nicipal hospital rather than in a primary one. Thus,
more systematic and comprehensive research needs to
be further conducted by expanding the study to include
nurses in primary hospitals where patients are crowded
too. However, the advantages of this study include such
as a high response rate, a relatively large sample size,
and that we revised and improved the threshold value
in the evaluation criteria job-related burnout, which
was defined by Zhu and colleagues [32, 33]. The revised
evaluation criteria take the three factors of job-related
burnout into account, not only facilitating a more com-
prehensive investigation of the situation of job-related
burnout, but also helping to take measures targeting
prevention and intervention. In addition, we applied
machine learning in the evaluation of risk factor im-
portance in job-related burnout, which provides a dir-
ection for health policy makers to make strategies to
prevent job-related burnout, for example, reducing
stress, enhancing GSE, and promoting communications
between individuals. Conversely, these strategies such

Table 4 Effects of GSE, neuroticism and stress on burnout in
multivariate regression analyses

Variable Model 1 Model 2 Model 3

β P value β P value β P value

stress 0.348 < 0.001 0.17 > 0.05 0.809 0.038

GSE −0.645 < 0.001 −0.979 0.005 0.181 > 0.05

N 0.587 < 0.001 0.913 > 0.05 6.032 0.029

stress×GSE 0.007 > 0.05 −0.017 > 0.05

stress×N −0.003 > 0.05 −0.102 0.046

GSE × N −0.007 > 0.05 −0.201 0.047

stress×GSE × N 0.004 0.045

Adjusted R2 0.266 0.264 0.267

ΔR2 0.268 < 0.001 0.001 > 0.05 0.003 0.045

β: standardized coefficient; GSE General self-efficacy, N Neuroticism

Fig. 3 Interaction of GSE, stress and neuroticism personality on burnout in nurses

Yao et al. BMC Health Services Research (2018) 18:667 Page 7 of 9

as enhancing GSE, psychiatric help and s

Statistics homework help

Auto Market Basket

Automobile Options
Engine Warranty Wheels Sound System Other Options
Slower Engine Faster engine fastest engine no warranty 3 year warranty 5 year warranty 15 inch 16 inch alloy am/fm amfm/dvd premium Sunroof Traction Control
1 0 0 0 1 0 0 1 0 0 0 1 1 1
0 1 0 0 1 0 0 0 1 1 0 0 0 0
0 0 1 0 0 1 1 0 0 0 1 0 1 1
0 0 1 0 0 1 0 1 0 0 0 1 0 1
0 1 0 0 0 1 1 0 0 1 0 0 0 1
0 1 0 0 1 0 0 1 0 0 1 0 1 1
1 0 0 0 1 0 1 0 0 1 0 0 0 0
1 0 0 1 0 0 0 1 0 0 1 0 1 1
0 1 0 0 0 1 0 0 1 0 1 0 0 0
0 0 1 0 1 0 0 1 0 0 0 1 1 1
0 1 0 0 0 1 0 0 1 0 1 0 0 1
1 0 0 0 1 0 0 1 0 0 0 1 1 0
0 1 0 0 1 0 0 1 0 1 0 0 0 1
1 0 0 0 1 0 0 0 1 0 1 0 0 1
0 1 0 0 1 0 0 1 0 0 1 0 1 0
0 0 1 0 0 1 0 1 0 0 0 1 1 1
0 0 1 0 0 1 0 1 0 0 1 0 0 0
0 1 0 0 1 0 0 1 0 0 1 0 1 1
0 0 1 0 1 0 0 0 1 0 1 0 0 1
1 0 0 0 0 1 0 0 1 0 1 0 1 1
0 1 0 0 0 1 0 0 1 1 0 0 1 0
1 0 0 0 1 0 0 1 0 0 1 0 0 1
0 0 1 0 0 1 1 0 0 0 0 1 1 0
0 1 0 0 0 1 1 0 0 0 0 1 1 1
1 0 0 0 0 1 1 0 0 1 0 0 0 0
0 0 1 0 0 1 0 1 0 0 1 0 0 1
0 1 0 0 1 0 1 0 0 0 1 0 0 1
0 1 0 0 0 1 0 1 0 1 0 0 0 0
1 0 0 0 1 0 0 1 0 0 1 0 0 0
1 0 0 0 1 0 0 0 1 0 1 0 0 1
1 0 0 0 1 0 1 0 0 0 1 0 0 0
1 0 0 1 0 0 0 1 0 0 1 0 0 1
0 1 0 0 0 1 0 1 0 0 1 0 1 1
0 1 0 0 1 0 0 1 0 0 1 0 0 1
0 1 0 0 1 0 0 0 1 0 1 0 0 0
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0 1 0 0 1 0 1 0 0 0 1 0 0 0
0 1 0 0 1 0 0 1 0 0 1 0 1 0
1 0 0 0 0 1 0 0 1 0 1 0 0 1
0 0 1 0 0 1 0 1 0 0 1 0 0 1
0 1 0 0 1 0 0 1 0 1 0 0 0 1
1 0 0 0 1 0 0 0 1 0 0 1 0 1
0 0 1 0 1 0 1 0 0 0 0 1 1 1
0 0 1 0 0 1 1 0 0 0 0 1 0 1
0 1 0 0 1 0 1 0 0 0 1 0 0 1
0 0 1 0 0 1 0 1 0 0 1 0 1 1

Statistics homework help

Data

Driver Points Poles Wins Top 5 Top 10 Winnings ($)
Tony Stewart 2403 1 5 9 19 6,529,870
Carl Edwards 2403 3 1 19 26 8,485,990
Kevin Harvick 2345 0 4 9 19 6,197,140
Matt Kenseth 2330 3 3 12 20 6,183,580
Brad Keselowski 2319 1 3 10 14 5,087,740
Jimmie Johnson 2304 0 2 14 21 6,296,360
Dale Earnhardt Jr. 2290 1 0 4 12 4,163,690
Jeff Gordon 2287 1 3 13 18 5,912,830
Denny Hamlin 2284 0 1 5 14 5,401,190
Ryan Newman 2284 3 1 9 17 5,303,020
Kurt Busch 2262 3 2 8 16 5,936,470
Kyle Busch 2246 1 4 14 18 6,161,020
Clint Bowyer 1047 0 1 4 16 5,633,950
Kasey Kahne 1041 2 1 8 15 4,775,160
A.J. Allmendinger 1013 0 0 1 10 4,825,560
Greg Biffle 997 3 0 3 10 4,318,050
Paul Menard 947 0 1 4 8 3,853,690
Martin Truex Jr. 937 1 0 3 12 3,955,560
Marcos Ambrose 936 0 1 5 12 4,750,390
Jeff Burton 935 0 0 2 5 3,807,780
Juan Montoya 932 2 0 2 8 5,020,780
Mark Martin 930 2 0 2 10 3,830,910
David Ragan 906 2 1 4 8 4,203,660
Joey Logano 902 2 0 4 6 3,856,010
Brian Vickers 846 0 0 3 7 4,301,880
Regan Smith 820 0 1 2 5 4,579,860
Jamie McMurray 795 1 0 2 4 4,794,770
David Reutimann 757 1 0 1 3 4,374,770
Bobby Labonte 670 0 0 1 2 4,505,650
David Gilliland 572 0 0 1 2 3,878,390
Casey Mears 541 0 0 0 0 2,838,320
Dave Blaney 508 0 0 1 1 3,229,210
Andy Lally* 398 0 0 0 0 2,868,220
Robby Gordon 268 0 0 0 0 2,271,890
J.J. Yeley 192 0 0 0 0 2,559,500

Statistics homework help

Data

Florida New York North Carolina
13 14 10
12 9 12
17 15 15
17 12 18
20 16 12
21 24 14
16 18 17
14 14 8
13 15 14
17 17 16
12 20 18
9 11 17
12 23 19
15 19 15
16 17 13
15 14 14
13 9 11
10 14 12
11 13 13
17 11 11

Statistics homework help

Northampton Community College
Introductory Statistics
Chapter 9 Project Confidence Intervals

SPRING 2022

Confidence Intervals

Introduction

In this project you will use Confidence Intervals to discover if new wood burning stoves generate less pollution than the old wood burning stoves. There is good data on the old wood burning stoves and the amount of pollution generated by the old stoves is well established. The new stoves have not been evaluated. Samples of air pollution are taken after the new stoves are installed. Since it is not yet established for the new stoves how much pollution they generate, Confidence Intervals are used based on the new data on the new stoves.

The four pollutant that are tested are particulate matter (PM), total carbon (TC), organic carbon (OC), which is carbon bound in organic molecules, and levoglucosan (LE).

The pollution output for the old stoves is given by the Baseline Levels. The baseline levels are compared with the levels of pollution generated by the new stoves. If the baseline level for the pollutant is within the confidence interval, there is no reason to believe the new stoves are different from the old stoves. But if the baseline number is not within the confidence interval, it is reasonable to assume that the level of pollution generated by the new stoves is different from the pollution levels of the old stoves. In particular, if the baseline number is higher—or above—the confidence interval, it is reasonable to conclude that the new stoves generate less pollution than the old stoves.

Baseline levels:

Particulate Matter (PM): 27.08 micrograms per cubic meter

Total Carbon (TC): 18.87 micrograms per cubic meter

Organic Carbon (OC): 17.41 micrograms per cubic meter

Leveglucosan (LE): 2.57 micrograms per cubic meter

Your project must have 8 boxplots, 8 confidence intervals and 8 conclusions. For each pollutant you will generate a boxplot based on the data in the Excel file. Then you will create a confidence interval. Finally you will decide if the new stove is generating more or less pollution than the old stove or if there is no difference. The decision is based on the baseline number in comparison with the confidence interval for the pollutant.

Code to complete the project is given on pages 5 and 6.

Data file: Chapter_9_Project_CI_Pollution.xlsx

Make sure you answer all questions in context and print out any outputs and graphs that you perform in R. These printouts will serve as justification for your work. For all probabilities round your answers to 4 decimal places. All graphs must have titles and labeled axes.

The town of Libby, Montana, has experienced high levels of air pollution in the winter because many of the homes in Libby are heated by wood stoves that produce a lot of pollution. In an attempt to reduce the level of air pollution in Libby, a program was undertaken in which almost every wood stove in the town was replaced with a newer, cleaner-burning model. Measurements of several air pollutants were taken both before and after the stove replacement. They included particulate matter (PM), total carbon (TC), organic carbon (OC), which is carbon bound in organic molecules, and levoglucosan (LE), which is a compound found in charcoal and is thus an indicator of the amount of wood smoke in the atmosphere.

In order to determine how much the pollution levels were reduced, scientists measured the levels of these pollutants for three winters prior to the replacement. The mean levels over this period of time are referred to as the
baseline levels
. Following are the baseline levels for these pollutants. The units are micrograms per cubic meter.

PM: 27.08 TC: 18.87 OC: 17.41 LE: 2.57

The data in Blackboard titled Chapter_9_Project_CI_Pollution.xlsx provides values measured on samples of winter days during the two years following replacement. For each pollutant, 20 measurements were taken. The first-year measurements are in PM1, OC1, TC1 and LE1. The second-year measurements are in PM2, OC2, TC2 and LE2.


Year 1

For each of the four pollutants measured in the first year following replacement– PM1, OC1, TC1 & LE1, complete the following and include graphs and statistics in your project.

1. Construct a boxplot for the values for Year 1 to verify that the assumptions for constructing a confidence interval are satisfied. [You should have one boxplot for each measure for a total of 4 boxplots.] Make sure you elaborate on these assumptions and use the boxplot to justify your results. [Do the boxplots show that the distribution of values is symmetrical?]

2. Report the median, mean and standard deviation for each sample.

3. Report the shape of the distribution of data. Is it symmetrical or skewed?

4. Construct a 95% confidence interval (CI) for the mean level of each pollutant for Year 1. Make sure you interpret each CI in context.

5. Based on the confidence interval, is it reasonable to conclude that the mean level in Year 1 was lower than the baseline level for the pollutant? Explain your results in context. [Use the confidence interval to decide. Is the baseline number within the confidence interval for the pollutant? If the baseline number is not within the confidence interval, what can you conclude?]


Year 2

The investigators were concerned that the reduction in pollution levels might be only temporary. Specifically, they were concerned that people might use their new stoves carefully at first, thus obtaining the full advantage of their cleaner burning, but then become more casual in their operation, leading to an increase in pollution levels. You will investigate this issue by constructing confidence intervals for the mean levels in Year 2. Again, 20 measurements were taken for each pollutant.

Repeat Steps 1 through 5 for each of the four pollutants in Year 2: PM2, OC2, TC2 & LE2. [Construct 4 boxplots using R. Construct 4 confidence intervals.]

Boxplots:

Function for boxplots:

boxplot(dataset$variable, main=”title”, xlab=”label x axis”, horizontal = T)

Example:

boxplot(Chapter_9_Project_CI_Pollution$PM1,main=”Particulate Matter Year 1”,xlab=”Particulate Matter”, horizontal=T)

Function for median: median(dataset$variable)

Example: median(Chapter_9_Project_CI_Pollution$PM1)

Function for mean: mean(dataset$variable)

Example: mean(Chapter_9_Project_CI_Pollution$PM1)

Function for standard deviation: sd(dataset$variable)

Example: sd(Chapter_9_Project_CI_Pollution$PM1)

Confidence Interval for µ when σ is unknown.

Given a simple random sample of size
n
with sample mean and sample standard deviation
s
, and assuming a normal distribution or large enough sample size, the confidence interval for µ when σ is unknown is:

where = sample mean of a random sample and = the margin of error.


M =


c = confidence level ( 0 < c < 1)

tc = critical value for confidence level c and degrees of freedom d.f. = n – 1

R code for Confidence Interval (σ is unknown) using t distribution.

Function for (Student) t-distribution critical value: qt(value of α/2, degrees of freedom)

Function for absolute value: abs(number or variable or function)

Function for square root: sqrt(number or variable or function)

Example:

alpha05 = 0.05 #specify confidence level 95%

n = 20

tcrit = abs(qt(alpha05/2, n-1)) #calculates the t-critical for confidence interval with

n – 1 d.f. when confidence level is 1-α

xbarPM1 = mean(Chapter_9_Project_CI_Pollution$PM1)

sPM1 = sd(Chapter_9_Project_CI_Pollution$PM1)

stderrPM1 = sPM1/sqrt(n) #calculates the standard error for sample mean

MEPM1= tcrit*stderrPM1 #calculates the margin of error

CIPM1 = c(xbarPM1-MEPM1, xbarPM1+MEPM1) #calculates the confidence interval

CIPM1 #prints out the confidence interval

Refer to page 40 in Introduction to Image result for r studio and R-Studio

____________________________________________________________________________

Proposed R code

Set values for t-critical value [Use same values for all pollutants—there is no need to repeat these lines of code for each pollutant]

> alpha05 = 0.05 #specify confidence level 95%

> n = 20

> tcrit = abs(qt(alpha05/2, n-1)) #calculates the t-critical for confidence interval with

n – 1 d.f. when confidence level is 1-α

Create Boxplot

> boxplot(Chapter_9_Project_CI_Pollution$PM1,main=”Particulate Matter Year 1”,xlab=”Particulate Matter”, horizontal=T)

Define variables for Normal Distribution function [median, mean and standard deviation]

> median(Chapter_9_Project_CI_Pollution$PM1) #median of PM1

> xbar = mean(Chapter_9_Project_CI_Pollution$PM1) #assign to mu value of mean of PM1

To display the mean, , , for the sample, type xbar on the command line and execute [press the ENTER key]

> xbar

> s = sd(Chapter_9_Project_CI_Pollution$PM1) #assign to s value of standard deviation of PM1

To display the standard deviation,
s
, for the sample, type s on the command line and execute [press the ENTER key]

> s

> stderr = s/sqrt(n) #calculates the standard error [standard deviation] for sample mean

Calculate margin of error and bounds for confidence interval

> ME= tcrit*stderr #calculates the margin of error

> CI = c(xbar-ME, xbar+ME) #calculates the confidence interval and assigns it to CI

> CI #prints out the confidence interval

To create the Boxplot and get the Confidence Interval for the other pollutants, repeat the code by reassigning
xbar
to mean of each sample and reassigning
s
to standard deviation of each sample. Then copy, paste, and execute the sequence of code above to get the Confidence Interval for the pollutant.

Statistics homework help

Base Data

Credit Risk Data
Loan Purpose Checking Savings Months Customer Months Employed Gender Marital Status Age Housing Years Job Credit Risk
Small Appliance $0 $739 13 12 M Single 23 Own 3 Unskilled Low
Furniture $0 $1,230 25 0 M Divorced 32 Own 1 Skilled High
New Car $0 $389 19 119 M Single 38 Own 4 Management High
Furniture $638 $347 13 14 M Single 36 Own 2 Unskilled High
Education $963 $4,754 40 45 M Single 31 Rent 3 Skilled Low
Furniture $2,827 $0 11 13 M Married 25 Own 1 Skilled Low
New Car $0 $229 13 16 M Married 26 Own 3 Unskilled Low
Business $0 $533 14 2 M Single 27 Own 1 Unskilled Low
Small Appliance $6,509 $493 37 9 M Single 25 Own 2 Skilled High
Small Appliance $966 $0 25 4 F Divorced 43 Own 1 Skilled High
Business $0 $989 49 0 M Single 32 Rent 2 Management High
New Car $0 $3,305 11 15 M Single 34 Rent 2 Unskilled Low
Business $322 $578 10 14 M Married 26 Own 1 Skilled Low
New Car $0 $821 25 63 M Single 44 Own 1 Skilled High
New Car $396 $228 13 26 M Single 46 Own 3 Unskilled Low
Used Car $0 $129 31 8 M Divorced 39 Own 4 Management Low
Furniture $652 $732 49 4 F Divorced 25 Own 2 Skilled High
New Car $708 $683 13 33 M Single 31 Own 2 Skilled Low
Repairs $207 $0 28 116 M Single 47 Own 4 Skilled Low
Education $287 $12,348 7 2 F Divorced 23 Rent 2 Skilled High
Furniture $0 $17,545 34 16 F Divorced 22 Own 4 Skilled High
Furniture $101 $3,871 13 5 F Divorced 26 Rent 4 Skilled High
Furniture $0 $0 25 23 M Married 19 Own 4 Skilled High
Furniture $0 $485 37 23 F Divorced 27 Own 2 Management High
New Car $0 $10,723 11 15 M Single 39 Rent 2 Unskilled Low
Business $141 $245 22 33 M Single 26 Own 3 Skilled Low
Used Car $0 $0 19 58 M Single 50 Other 4 Skilled High
Used Car $2,484 $0 49 46 M Single 34 Other 1 Skilled Low
Small Appliance $237 $236 37 24 M Single 23 Rent 4 Skilled Low
Small Appliance $0 $485 19 12 M Single 23 Own 2 Skilled Low
Education $335 $1,708 37 7 M Single 46 Other 4 Skilled High
Small Appliance $3,565 $0 31 32 M Single 35 Own 3 Skilled Low
Small Appliance $0 $407 13 2 F Divorced 28 Own 2 Skilled Low
Business $16,647 $895 16 34 M Single 25 Rent 4 Skilled Low
Business $0 $150 49 46 F Divorced 36 Rent 4 Skilled High
Small Appliance $0 $490 5 41 M Single 41 Own 1 Unskilled Low
Furniture $0 $162 25 1 M Divorced 54 Own 1 Skilled High
Small Appliance $940 $715 9 40 F Divorced 43 Own 2 Unskilled Low
Small Appliance $0 $323 49 42 M Married 33 Own 1 Skilled High
New Car $0 $128 13 74 M Single 34 Own 3 Skilled High
Other $218 $0 49 0 M Single 39 Other 4 Unemployed Low
Used Car $0 $109 25 26 M Single 34 Own 3 Unskilled Low
Small Appliance $16,935 $189 37 60 M Single 30 Own 2 Skilled Low
Furniture $664 $537 31 33 M Single 48 Own 2 Skilled High
Furniture $150 $6,520 12 1 F Divorced 19 Own 1 Skilled Low
Small Appliance $0 $138 7 119 M Married 29 Rent 2 Skilled Low
Furniture $216 $0 19 3 F Divorced 26 Rent 3 Skilled High
New Car $0 $660 17 75 M Single 42 Rent 4 Skilled High
Business $0 $724 25 8 M Single 30 Rent 2 Skilled High
Small Appliance $0 $897 19 5 M Married 38 Own 4 Skilled Low
Small Appliance $265 $947 25 5 M Married 21 Own 1 Skilled High
Furniture $4,256 $0 16 36 F Divorced 32 Rent 4 Unskilled Low
Business $870 $917 28 6 M Single 35 Own 2 Skilled High
New Car $162 $595 22 10 M Divorced 46 Own 4 Skilled Low
Used Car $0 $789 25 28 M Single 37 Own 3 Management Low
Education $0 $0 37 114 M Single 39 Own 4 Management High
Furniture $0 $746 13 16 F Divorced 29 Own 3 Skilled Low
New Car $461 $140 19 32 M Single 27 Rent 3 Unskilled Low
New Car $0 $659 19 5 F Divorced 22 Rent 3 Skilled High
Furniture $0 $717 37 60 M Single 40 Own 2 Skilled High
New Car $0 $667 29 10 M Single 44 Own 2 Unskilled High
New Car $580 $0 11 8 M Single 26 Own 4 Unskilled High
Small Appliance $0 $763 13 46 F Divorced 57 Own 3 Unskilled Low
New Car $0 $1,366 19 17 M Single 34 Own 4 Unskilled Low
Small Appliance $0 $552 25 4 M Married 47 Own 4 Skilled High
Small Appliance $0 $14,643 16 115 M Single 46 Own 3 Skilled Low
Business $758 $2,665 13 31 M Single 38 Own 4 Unskilled Low
Used Car $399 $0 31 0 F Divorced 52 Own 1 Management High
Furniture $513 $442 7 0 M Single 34 Own 1 Management Low
Furniture $0 $8,357 25 5 M Single 29 Other 4 Skilled High
New Car $0 $0 22 9 M Single 39 Own 2 Unskilled High
Small Appliance $565 $863 10 81 M Single 36 Own 4 Unskilled Low
Business $0 $322 28 28 M Single 25 Own 4 Skilled Low
Furniture $0 $800 13 69 M Single 59 Own 3 Skilled High
Small Appliance $0 $656 37 85 M Single 27 Own 2 Skilled Low
New Car $166 $922 13 2 F Divorced 24 Rent 1 Skilled High
Business $9,783 $885 13 3 F Divorced 25 Own 1 Unemployed High
Business $674 $2,886 49 32 M Single 29 Own 2 Skilled Low
Repairs $0 $626 43 0 M Single 64 Own 4 Unemployed Low
Business $15,328 $0 25 9 M Single 31 Own 4 Skilled Low
New Car $0 $904 12 6 M Single 38 Own 4 Unskilled Low
Education $713 $784 61 17 M Single 41 Other 4 Skilled High
New Car $0 $806 19 3 F Divorced 22 Own 2 Unskilled High
Education $0 $3,281 19 20 F Divorced 29 Own 2 Skilled High
New Car $0 $759 16 59 M Single 32 Rent 3 Skilled High
Small Appliance $0 $680 25 3 F Divorced 34 Own 4 Skilled High
Used Car $0 $104 37 25 M Single 23 Own 4 Skilled High
Small Appliance $303 $899 13 3 M Single 21 Own 1 Skilled High
Small Appliance $900 $1,732 37 11 F Divorced 49 Other 4 Skilled High
Furniture $0 $706 31 14 M Divorced 31 Own 2 Skilled Low
Education $1,257 $0 10 65 F Divorced 40 Rent 4 Unskilled Low
Small Appliance $0 $576 7 14 F Divorced 28 Own 1 Skilled Low
Repairs $273 $904 7 2 M Married 21 Own 1 Unskilled Low
Business $522 $194 25 79 M Divorced 30 Own 4 Skilled High
Small Appliance $0 $710 25 1 F Divorced 37 Own 3 Skilled Low
Small Appliance $0 $5,564 25 93 M Single 33 Own 2 Skilled Low
Small Appliance $0 $192 46 13 M Single 22 Other 4 Skilled High
New Car $0 $637 13 21 F Divorced 23 Own 2 Unskilled High
Small Appliance $514 $405 49 13 F Divorced 21 Own 2 Skilled High
Furniture $457 $318 19 108 M Single 40 Own 1 Skilled Low
Small Appliance $5,133 $698 19 14 M Single 36 Own 2 Skilled High
New Car $0 $369 10 16 M Single 29 Own 1 Skilled Low
Retraining $644 $0 13 88 M Single 37 Own 4 Skilled Low
Furniture $305 $492 19 1 F Divorced 26 Own 1 Skilled Low
New Car $9,621 $308 25 41 M Single 37 Other 3 Skilled High
Education $0 $127 13 22 M Single 39 Rent 4 Unskilled High
Business $0 $565 19 14 M Married 27 Own 2 Skilled High
Furniture $0 $12,632 16 9 F Divorced 19 Rent 4 Skilled Low
New Car $0 $116 49 45 M Single 45 Other 4 Skilled High
Used Car $0 $178 13 89 M Single 34 Other 4 Skilled High
Small Appliance $6,851 $901 13 21 F Divorced 43 Rent 2 Unskilled Low
Furniture $13,496 $650 19 20 M Single 33 Own 1 Unskilled High
Business $509 $241 25 14 M Single 35 Own 4 Unskilled High
Used Car $0 $609 37 6 M Single 31 Other 2 Management Low
Furniture $19,155 $131 25 24 M Single 25 Own 2 Skilled Low
Furniture $0 $544 19 15 F Divorced 27 Own 2 Skilled Low
Small Appliance $0 $10,853 25 81 F Divorced 56 Rent 4 Management Low
Used Car $374 $0 25 14 M Single 45 Own 4 Management Low
Large Appliance $0 $409 49 15 M Single 53 Own 4 Skilled High
Furniture $828 $391 9 12 F Divorced 23 Own 4 Skilled High
Furniture $0 $322 13 9 F Divorced 25 Own 1 Skilled Low
Small Appliance $829 $583 7 18 F Divorced 63 Own 3 Skilled Low
Small Appliance $0 $12,242 25 53 M Single 34 Own 2 Skilled High
Furniture $0 $479 19 0 M Single 24 Own 1 Unemployed High
New Car $939 $496 19 56 M Single 35 Own 4 Skilled High
New Car $0 $466 25 42 M Single 30 Own 3 Skilled High
New Car $889 $1,583 37 79 M Single 29 Other 3 Skilled Low
Furniture $876 $1,533 31 21 F Divorced 20 Rent 4 Skilled High
Small Appliance $893 $0 16 94 M Single 49 Own 4 Skilled Low
Business $12,760 $4,873 13 73 M Single 56 Rent 4 Unskilled Low
Furniture $0 $0 13 94 M Single 48 Rent 4 Skilled Low
Small Appliance $0 $717 22 10 F Divorced 24 Own 2 Skilled High
Small Appliance $959 $7,876 28 20 M Single 22 Own 2 Unskilled High
Small Appliance $0 $4,449 25 87 M Single 30 Own 4 Skilled High
Other $0 $0 25 54 M Single 39 Own 3 Management High
Business $0 $104 25 23 M Married 20 Own 2 Unskilled Low
Repairs $0 $897 19 2 F Divorced 22 Own 4 Skilled High
New Car $698 $4,033 16 20 M Married 24 Rent 2 Skilled High
Furniture $0 $945 13 6 M Divorced 41 Own 1 Skilled Low
Furniture $0 $836 25 99 M Single 32 Own 4 Skilled Low
Small Appliance $0 $325 19 13 F Divorced 23 Own 2 Skilled High
Small Appliance $12,974 $19,568 13 7 F Divorced 41 Rent 3 Skilled Low
Furniture $0 $803 13 89 M Single 52 Other 4 Management High
Small Appliance $317 $10,980 13 17 M Single 65 Own 3 Unskilled High
Business $0 $265 13 10 F Divorced 26 Own 2 Skilled Low
Repairs $0 $609 31 3 M Divorced 33 Own 1 Unskilled High
Small Appliance $0 $1,851 12 0 F Divorced 56 Own 4 Unskilled Low
Furniture $192 $199 25 5 F Divorced 24 Own 4 Unskilled High
New Car $0 $500 28 7 F Divorced 20 Rent 3 Skilled High
New Car $0 $509 16 3 M Single 35 Own 3 Skilled Low
Used Car $0 $270 25 25 M Single 34 Own 3 Skilled Low
New Car $0 $457 13 63 M Single 38 Own 4 Management Low
Used Car $0 $260 25 78 M Single 34 Own 4 Management Low
New Car $942 $3,036 25 36 M Single 37 Own 3 Skilled Low
Small Appliance $0 $643 19 6 M Single 31 Other 2 Management Low
New Car $3,329 $0 19 15 M Single 67 Rent 4 Skilled High
Used Car $0 $6,345 25 19 M Single 26 Own 2 Skilled Low
Education $0 $922 37 9 F Divorced 24 Own 2 Management High
Furniture $0 $909 25 3 M Single 21 Other 1 Skilled Low
Large Appliance $0 $775 19 8 M Married 46 Own 3 Unskilled High
Furniture $0 $979 25 48 M Single 22 Rent 4 Skilled High
Furniture $0 $948 19 2 F Divorced 20 Rent 4 Skilled Low
Business $339 $2,790 22 55 M Divorced 60 Rent 2 Unskilled High
Used Car $0 $309 49 37 M Single 25 Own 3 Skilled Low
Small Appliance $0 $762 10 1 F Divorced 21 Rent 4 Skilled High
Small Appliance $0 $970 13 14 F Divorced 22 Own 1 Skilled Low
Used Car $105 $320 28 54 M Single 29 Own 2 Management Low
Small Appliance $0 $861 13 111 M Single 56 Own 4 Unskilled High
Repairs $216 $262 37 2 M Single 32 Rent 1 Unskilled High
Furniture $113 $692 11 14 M Divorced 30 Own 2 Unskilled Low
Used Car $109 $540 37 1 M Married 27 Rent 4 Management High
New Car $0 $470 13 0 F Divorced 37 Own 2 Unemployed Low
New Car $0 $192 7 2 M Single 39 Own 4 Unskilled Low
New Car $8,176 $12,230 7 5 M Married 26 Own 2 Unemployed Low
Repairs $0 $772 25 19 M Divorced 32 Own 2 Skilled Low
Furniture $468 $14,186 22 24 M Single 31 Own 2 Skilled Low
Used Car $7,885 $6,330 16 14 M Single 35 Own 2 Skilled Low
Small Appliance $0 $18,716 19 93 M Single 31 Own 3 Management Low
New Car $0 $886 22 96 M Single 64 Own 4 Skilled Low
Business $0 $750 37 2 M Divorced 27 Own 1 Skilled High
Small Appliance $0 $3,870 25 11 F Divorced 31 Own 2 Unskilled High
Small Appliance $0 $3,273 13 4 M Married 32 Own 3 Unskilled High
Business $0 $406 6 35 M Single 73 Own 4 Unskilled Low

Statistics homework help

Data

Florida New York North Carolina
3 8 10
7 11 7
7 9 3
3 7 5
8 8 11
8 7 8
8 8 4
5 4 3
5 13 7
2 10 8
6 6 8
2 8 7
6 12 3
6 8 9
9 6 8
7 8 12
5 5 6
4 7 3
7 7 8
3 8 11

Statistics homework help

Regression Modeling Data

FloorArea (Sq.Ft.) Offices Entrances Age AssessedValue ($’000)
4790 4 2 8 1796
4720 3 2 12 1544 The Excel file for this assignment contains a database with information about the tax assessment value assigned to medical office buildings in a city. The following is a list of the variables in the database:
5940 4 2 2 2094 FloorArea: square feet of floor space
5720 4 2 34 1968 Offices: number of offices in the building
3660 3 2 38 1567 Entrances: number of customer entrances
5000 4 2 31 1878 Age: age of the building (years)
2990 2 1 19 949 AssessedValue: tax assessment value (thousands of dollars)
2610 2 1 48 910 Use the data to construct a model that predicts the tax assessment value assigned to medical office buildings with specific characteristics.
5650 4 2 42 1774 Construct a scatter plot in Excel with FloorArea as the independent variable and AssessmentValue as the dependent variable. Insert the bivariate linear regression equation and r^2 in your graph. Do you observe a linear relationship between the 2 variables?
3570 2 1 4 1187 Use Excel’s Analysis ToolPak to conduct a regression analysis of FloorArea and AssessmentValue. Is FloorArea a significant predictor of AssessmentValue?
2930 3 2 15 1113 Construct a scatter plot in Excel with Age as the independent variable and AssessmentValue as the dependent variable. Insert the bivariate linear regression equation and r^2 in your graph. Do you observe a linear relationship between the 2 variables?
1280 2 1 31 671 Use Excel’s Analysis ToolPak to conduct a regression analysis of Age and Assessment Value. Is Age a significant predictor of AssessmentValue?
4880 3 2 42 1678 Construct a multiple regression model.
1620 1 2 35 710 Use Excel’s Analysis ToolPak to conduct a regression analysis with AssessmentValue as the dependent variable and FloorArea, Offices, Entrances, and Age as independent variables. What is the overall fit r^2? What is the adjusted r^2?
1820 2 1 17 678 Which predictors are considered significant if we work with α=0.05? Which predictors can be eliminated?
4530 2 2 5 1585 What is the final model if we only use FloorArea and Offices as predictors?
2570 2 1 13 842 Suppose our final model is:
4690 2 2 45 1539 AssessedValue = 115.9 + 0.26 x FloorArea + 78.34 x Offices
1280 1 1 45 433 What wouldbe the assessed value of a medical office building with a floor area of 3500 sq. ft., 2 offices, that was built 15 years ago? Is this assessed value consistent with what appears in the database?
4100 3 1 27 1268 Submit your assignment in Excel. Answer all questions in the Excel workbook. Please do not submit a separate Word document.
3530 2 2 41 1251
3660 2 2 33 1094
1110 1 2 50 638
2670 2 2 39 999
1100 1 1 20 653
5810 4 3 17 1914
2560 2 2 24 772
2340 3 1 5 890
3690 2 2 15 1282
3580 3 2 27 1264
3610 2 1 8 1162
3960 3 2 17 1447

Statistics homework help

Article

Wholesome Foods and Wholesome
Morals? Organic Foods Reduce Prosocial
Behavior and Harshen Moral Judgments

Kendall J. Eskine
1

Abstract

Recent research has revealed that specific tastes can influence moral processing, with sweet tastes inducing prosocial behavior
and disgusting tastes harshening moral judgments. Do similar effects apply to different food types (comfort foods, organic foods,
etc.)? Although organic foods are often marketed with moral terms (e.g., Honest Tea, Purity Life, and Smart Balance), no
research to date has investigated the extent to which exposure to organic foods influences moral judgments or behavior. After
viewing a few organic foods, comfort foods, or control foods, participants who were exposed to organic foods volunteered
significantly less time to help a needy stranger, and they judged moral transgressions significantly harsher than those who
viewed nonorganic foods. These results suggest that exposure to organic foods may lead people to affirm their moral identities,
which attenuates their desire to be altruistic.

Keywords

morality, prosociality, organic food, moral licensing, embodied cognition

Organic foods, which are typically the products of ethical and

environmentally friendly practices, are often marketed with

moral terms (e.g., Honest Tea, Purity Life, Smart Balance,

etc.). Is this just a marketing strategy, a linguistic coincidence,

or do people’s conceptual representations of organic food and

morality actually share the same mental space? Some research

suggests that exposure to different types of tastes and foods can

influence higher order judgments involved with complex

domains like morality and prosocial behavior.

In the domain of taste, Meier, Moeller, Riemer-Peltz, and

Robinson (2012) revealed that people were more willing to

help others after tasting something sweet, whereas Eskine,

Kacinik, and Prinz (2011) showed that disgusting tastes can

lead to harsher moral judgments. In the domain of food, Trisoli

and Gabriel (2011) found that exposure to comfort foods like

chicken soup alleviated feelings of loneliness, and Bastian,

Loughnan, Haslam, and Radke (2012) revealed that the extent

to which meat-eaters attributed moral status to animals

depended largely on whether they were likely to consume those

animals. For example, animals that were perceived as highly

edible (e.g., chicken, cow, and fish) were judged to be signifi-

cantly less capable of possessing various mental capacities

(e.g., morality, pain, pleasure, memory, emotion, etc.) than ani-

mals that were perceived as inedible (e.g., mole, rat, and sloth).

While the above research highlights how our daily interac-

tions with different foods and tastes can influence moral pro-

cessing, no research to date has experimentally investigated

the extent to which exposure to organic foods influences moral

behavior and moral judgments. In order to test whether

exposure to organic food does in fact give rise to the moral

superiority suggested by its marketing, participants were

exposed to one of the three different food types (organic, com-

fort, or control) prior to receiving an opportunity to help a

needy other and making moral judgments.

Two outcomes are likely with respect to organic food.

Drawing from Schnall, Roper, and Fessler’s (2010) research

on feelings of elevation, one possibility is that exposure to

organic foods will make participants feel good about them-

selves and therefore subsequently engage in more altruistic

acts, which would result in greater volunteerism and kinder

moral judgments. On the other hand, the second possibility

would make opposite predictions.

Rozin (1999) argued that moralization takes place when pre-

ferences are transformed into values, a process that often

occurs in health domains (e.g., cigarette smoking, drugs, etc.).

Going beyond mere marketing terms, there are at least two pos-

sible routes that may lead organic food exposure to increase the

salience of one’s moral identity. The first route leads people to

1
Department of Psychological Sciences, Loyola University New Orleans, New

Orleans, LA, USA

Corresponding Author:

Kendall J. Eskine, Department of Psychological Sciences, Loyola University New

Orleans, Box 194, 6363 Saint Charles Avenue, New Orleans, LA 70118, USA.

Email: kjeskine@loyno.edu

Social Psychological and
Personality Science
4(2) 251-254
ª The Author(s) 2012
Reprints and permission:
sagepub.com/journalsPermissions.nav
DOI: 10.1177/1948550612447114
spps.sagepub.com

moralize their preferences for organic foods for reasons of

health, what some might consider ‘‘moral expansion’’ (Rozin,

1997). The second route leads people to moralize their prefer-

ences for organic foods because it is viewed as a morally super-

ior choice for the environment, which is an example of ‘‘moral

piggybacking’’ (Rozin, 1997). While it is also possible that

some people could take both routes, the resulting moralization

processes should similarly cause individuals’ moral identities

to become more salient when being exposed to organic foods.

Based on the research from moral licensing, which indicates

that people are less likely to act altruistically when their moral
identities are salient (Sachdeva, Iliev, & Medin, 2009), the

present research predicts that those exposed to organic foods

would help less and make harsher moral judgments compared

to those exposed to nonorganic foods.

Method

Sixty-two Loyola University undergraduates (37 females and 25

males) participated in the present experiment for course credit and

were randomly assigned to one of the three food conditions

(organic, comfort, and control) in a between-subjects design. Told

that they were participating in two unrelated studies (a consumer

research survey about food desirability and a separate moral judg-

ment task), participants were first given a packet containing four

counterbalanced pictures of food items from one of the following

categories: organic foods with organic food labels (apple, spi-

nach, tomato, and carrot), comfort foods (ice cream, cookie, cho-

colate, and brownie), or control foods (oatmeal, rice, mustard, and

beans) (see Figure 1). Participants also rated each food item on a

7-point scale (1 ¼ not at all desirable to 7 ¼ very desirable) to
help corroborate the cover story as well as provide information

about their personal food preferences. All food items were chosen

based on survey results from a separate sample of participants (N

¼ 28, 16 females) during which they rated a variety of foods on a
7-point scale (1 ¼ typical comfort food, 4 ¼ neither comfort nor
organic food, 7 ¼ typical organic food), giving the following

results for organic foods (M ¼ 6.61, SD ¼ 1.17), comfort foods
(M ¼ 1.54, SD¼ .98), and neither comfort nor organic and hence
‘‘control’’ foods (M ¼ 4.32, SD ¼ 1.37).

Participants next received a packet containing six counter-

balanced moral transgressions describing second cousins enga-

ging in consensual incest, a man eating his already-dead dog, a

congressman accepting bribes, a lawyer prowling hospitals

for victims, a person shoplifting, and a student stealing library

books (Wheatley & Haidt, 2005). Each moral judgment was

indicated on a 7-point scale (1 ¼ not at all morally wrong
to 7 ¼ very morally wrong). As with previous research
(Eskine, Kacinik, & Prinz, 2011), all judgments were aver-

aged into a single score.

After next answering demographic questions, participants

were told ‘‘that another professor from another department is

also conducting research and really needs volunteers.’’ They

were informed that they would not receive course credit or

compensation for their help and were asked to indicate how

many minutes (of the 30) they would be willing to volunteer

(a commonly used measure of prosocial behavior, Meier et

al., 2012). All participants were debriefed and probed for sus-

picion, although no participants indicated any awareness of the

experiment’s purpose.

Results

A between-subjects analysis of variance (ANOVA) revealed an

overall effect of food type on prosocial behavior, F(2, 59) ¼
8.894, p < .001, Zp

2 ¼ .232, and a follow-up Tukey’s honestly
significant difference (HSD) test showed that those exposed to

organic food volunteered significantly less time (n ¼ 20, M ¼
13.40, SD ¼ 9.38.) than those exposed to control foods (n ¼ 20,
M ¼ 19.88, SD ¼ 10.33), p < .05, or comfort foods (n ¼ 22,
M ¼ 24.55, SD ¼ 5.49), p < .001, with the latter two groups not
significantly differing (see Table 1). To demonstrate that these

effects were driven by organic food exposure and not the sub-

jective desirability of each food item, each participant’s four

Apple Ice Cream Mustard

Figure 1. Example food item pictures from the organic, comfort, and control conditions, respectively.

252 Social Psychological and Personality Science 4(2)

food desirability ratings were averaged into an overall desir-

ability score, which was then treated as a covariate. The result

of this analysis of covariance (ANCOVA) was still significant,

F(2, 58) ¼ 8.042, p ¼ .001, Zp2 ¼ .217, thus ruling out the
effects of subjective food desirability.

A separate ANOVA on averaged moral judgments indicated

an overall effect of food type, F(2, 59) ¼ 7.516, p ¼ .001,
Zp

2 ¼ .203, and a follow-up Tukey’s HSD test showed that
those exposed to organic food made significantly harsher

moral judgments (M ¼ 5.58, SD ¼ .59) than those exposed
to control foods (M ¼ 5.08, SD ¼ .62), p < .05, or comfort
foods (M ¼ 4.89, SD ¼ .57), p ¼ .001, with the latter two
groups not significantly differing (see Table 1). An ANCOVA

was conducted with desirability as a covariate and still

revealed a significant effect of food type, F(2, 58) ¼ 7.210,
p ¼ .002, Zp2 ¼ .199, indicating that food desirability did not
play a significant role in moral judgment.

Discussion

Together, these findings reveal that organic foods and morality

do share the same conceptual space. As predicted, the findings

showed that exposure to ethical and environmentally friendly

foods resulted in reduced prosocial behavior and harsher

moral judgments. Importantly, the results also indicated that

participants’ food preferences did not influence their prosoci-

ality or moral judgments, thus ruling out subjective desirabil-

ity in the present research. Therefore, the present research

suggests that exposure to organic foods helps people affirm

their moral identities and attenuates their desire to be altruis-

tic, as found by Sachdeva, Iliev, and Medin (2009). In a sim-

ilar vein, Mazar and Zhong (2010) provide evidence for such a

view. In particular, they found that participants were more

likely to cheat and steal after purchasing ‘‘green’’ rather than

conventional products. Since green and organic products

share many commonalities, it seems likely that environmen-

tally friendly products can actually affect the salience of one’s

moral identity and induce moral licensing.

Drawing from Rozin (1997, 1999), two mechanisms were

described to explain how exposure to organic foods might

affirm individuals’ moral identities. According to the moral

expansion route, some might moralize their preferences for

organic foods for health reasons, whereas the moral piggyback-

ing route asserts that others might moralize organic food

because it is perceived as a morally superior choice for the

environment, other organisms, and so on. While it is possible

that one could simultaneously endorse both routes, they each

have different theoretical implications. The moral expansion

route proposes that moralization is carried by cognitive-

rational processes, whereas the moral piggybacking route is

carried by affective processes (Rozin, 1999). Accordingly,

these routes might lead us to make different predictions about

the extent to which exposure to organic food affirms individu-

als’ moral identities and enables moral licensing.

Classic findings in persuasion and attitude formation may

shed light on this issue (Petty & Cacioppo, 1984). It is well

documented that long-lasting attitude change is a product of

cognitive-rational processes (central route) rather than affec-

tive processes (peripheral route). Given that both the moraliza-

tion and the persuasion approaches position cognitive and

affective information in distinct channels, similar patterns

might occur in moralization processes. For example, while

both routes can lead to moralization of organic food in gen-

eral, those who moralize in cognitive formats might be more

likely to experience moral licensing than those who moralize

in affective formats because, for them, organic food repre-

sents a deliberate choice (rather than a mere emotional asso-

ciation) in a domain that is meaningful to them, which

further strengthens the salience of their moral identities after

exposure to organic food. Although the present research did

not assess participants’ cognitive and affective attitudes

toward organic food, this raises important empirical questions

and warrants further investigation.

What does this mean for organic marketing? Should

advertisers be cautious of how hard they ‘‘push’’ the branding

of their products? One possibility is that those who simply

purchase organic products will be less likely to engage in

other meaningful acts of environmental protection. Although

organic products are indubitably environmentally sound and

ethical choices, perhaps milder, more subtle advertisements

could help promote the beneficial qualities of these products

without inadvertently inducing moral licensing in its

consumers.

Further, given the general nutritional differences and bodily

effects of prototypical comfort and organic foods, future

research should also explore whether actually consuming

organic or comfort food differentially influences moral beha-

viors. While the results from the comfort food condition did not

significantly differ from the control condition, the trends sug-

gest that comfort food exposure can induce more prosocial

behavior and kinder moral judgments, which is compatible

with previous descriptions of comfort food as a ‘‘social surro-

gate’’ (Trisoli & Gabriel, 2011). According to this view, com-

fort foods help connect people in a way that fosters

Table 1. Participants’ Prosocial Behavior (in Minutes) and Moral Judgments as a Function of Food Type.

Condition Organic Food Control Food Comfort Food

Prosocial behavior 13.40 (9.38) 19.88 (10.33) 24.55 (5.49)
Moral judgment 5.58 (0.59) 5.08 (0.62) 4.89 (0.57)

Mean ratings of prosocial behavior and moral judgments in each condition with standard deviations in parentheses. Higher values in the prosocial and moral judg-
ment variables indicate minutes willing to help and harsher moral judgments, respectively.

Eskine 253

interpersonal warmth. Therefore, differentiating the effects of

organic and comfort food exposure and consumption remains

an important avenue for future research.

More generally, these results are important because food is a

fundamental part of everyone’s life, and as food choices continue

to expand we should explore its psychological consequences.

People celebrate with food, plan their days around it, and even

organize romantic encounters along various confectionary

delights. Even beyond first dates and lunch breaks, food can also

connect people to their heritage. Recipes can convey information

about a family’s history, its geography, and its relationship to the

environment. Despite its ubiquity in daily life, food has been

vastly underexplored in the psychological sciences, although

important strides have been made recently (Zhong & DeVoe,

2010). For example, Schuldt, Muller, and Schwarz (in press)

found that participants judged chocolate to contain fewer calories

when it was described as fair trade (Study 1) or as treating its

workers ethically (Study 2) when compared to chocolates with

no such descriptions. Taken together, this research has consider-

able implications for understanding how our foods choices and

experiences shape more than just our nutrition.

As Paul Rozin (1996, p. 18) noted, ‘‘Food progresses from

being a source of nutrition and sensory pleasure to being a

social marker, an aesthetic experience, a source of meaning and

metaphor, and, often, a moral entity.’’ Indeed, future research

should investigate food and its corresponding embodied states,

which might serve as an important primary metaphor (Lakoff

& Johnson, 1999) that affects the representation, processing,

and development of our moral conceptual architecture.

Acknowledgments

The author thanks Nick Dondzila, David Garcia, Samantha Montano,

and Erica Wright for their help with data collection. The author is

especially grateful to Brian Meier, Paula Niedenthal, and two anon-

ymous reviewers for their thoughtful comments on an earlier version

of this draft.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to

the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, author-

ship, and/or publication of this article.

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254 Social Psychological and Personality Science 4(2)

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Statistics homework help

EClinicalMedicine 24 (2020) 100424

Contents lists available at ScienceDirect

EClinicalMedicine

journal homepage: https://www.journals.elsevier.com/eclinicalmedicine

Research Paper

Frontline nurses’ burnout, anxiety, depression, and fear statuses and
their associated factors during the COVID-19 outbreak in Wuhan, China:
A large-scale cross-sectional study

Deying Hua,1, Yue Kongb,1, Wengang Lic,1, Qiuying Hand,1, Xin Zhange, Li Xia Zhuf,
Su Wei Wanf, Zuofeng Liuc, Qu Shenc, Jingqiu Yangc, Hong-Gu Hef,*, Jiemin Zhuc,*
a Department of Nursing, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, Hubei Province, PR China
b Department of Nursing, the 900th Hospital of Joint Logistic Support Force, PLA, Fuzhou, Fujian, PR China
c School of Medicine, Xiamen University, Xiamen, Fujian, PR China
d Department of Nursing, Zhongshan Hospital, Xiamen University, Xiamen, Fujian, PR China
e Department of Nursing, Fifth Medical Center of PLA General Hospital, Beijing, PR China
f Alice Lee Centre for Nursing Studies, Yong Loo Lin School of Medicine, National University of Singapore, Singapore, National University Health System, Singapore

A R T I C L E I N F O

Article History:
Received 16 May 2020
Revised 31 May 2020
Accepted 2 June 2020
Available online 27 June 2020

* Corresponding authors.
E-mail addresses: nurhhg@nus.edu.sg (H.-G. He), jiem

1 These authors contributed equally to this work.

https://doi.org/10.1016/j.eclinm.2020.100424
2589-5370/© 2020 The Author(s). Published by Elsevier

A B S T R A C T

Background: During the Coronavirus Disease 2019 (COVID-19) pandemic, frontline nurses face enormous
mental health challenges. Epidemiological data on the mental health statuses of frontline nurses are still lim-
ited. The aim of this study was to examine mental health (burnout, anxiety, depression, and fear) and their
associated factors among frontline nurses who were caring for COVID-19 patients in Wuhan, China.
Methods: A large-scale cross-sectional, descriptive, correlational study design was used. A total of 2,014 eligible
frontline nurses from two hospitals in Wuhan, China, participated in the study. Besides sociodemographic and
background data, a set of valid and reliable instruments were used to measure outcomes of burnout, anxiety,
depression, fear, skin lesion, self-efficacy, resilience, and social support via the online survey in February 2020.
Findings: On average, the participants had a moderate level of burnout and a high level of fear. About half of
the nurses reported moderate and high work burnout, as shown in emotional exhaustion (n = 1,218, 60.5%),
depersonalization (n = 853, 42.3%), and personal accomplishment (n = 1,219, 60.6%). The findings showed
that 288 (14.3%), 217 (10.7%), and 1,837 (91.2%) nurses reported moderate and high levels of anxiety, depres-
sion, and fear, respectively. The majority of the nurses (n = 1,910, 94.8%) had one or more skin lesions, and
1,950 (96.8%) nurses expressed their frontline work willingness. Mental health outcomes were statistically
positively correlated with skin lesion and negatively correlated with self-efficacy, resilience, social support,
and frontline work willingness.
Interpretation: The frontline nurses experienced a variety of mental health challenges, especially burnout and
fear, which warrant attention and support from policymakers. Future interventions at the national and
organisational levels are needed to improve mental health during this pandemic by preventing and manag-
ing skin lesions, building self-efficacy and resilience, providing sufficient social support, and ensuring front-
line work willingness.

© 2020 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND
license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Keywords:

Covid-19
Frontline nurses
Mental health
Burnout
Anxiety
Depression
Fear
China

inzhu@xmu.edu.cn (J. Zhu).

Ltd. This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)

1. Introduction

The pandemic of Coronavirus Disease 2019 (COVID-19) is cur-
rently a major global public health emergency [1]. By 27 March 2020,
there were 465,915 confirmed cases in 199 countries, and 21,031

people had lost their lives [2]. The outbreak of COVID-19 put global
and national healthcare systems to test, which when overwhelmed,
can severely compromise the well-being of frontline healthcare
workers (HCWs) [3].

Since the first COVID-19 case was reported in December 2019 in
Wuhan [4], approximately 42,000 HCWs, including 28,600 nurses all
over China, were sent to Hubei Province to assist local healthcare
teams to care for COVID-19 patients [5]. A study revealed that HCWs
who were working in Wuhan often felt stress, depression, and anxi-
ety, but this study didn’t target specially at frontline nurses [6].

Research in context

Evidence before this study

The outbreak of COVID-19 put global and national healthcare
systems to test, which when overwhelmed, can severely com-
promise the well-being of frontline healthcare workers
(HCWs). We searched electronic databases, including CINAHL,
PubMed, Google Scholar, and the China National Knowledge
Infrastructure, for articles that were published in either English
or Chinese from 1 January 2003 to 12 February 2020, using the
following keywords: disease outbreak, pandemic, medical cri-
ses, quality of life, self-efficacy, resilience, social support,
fatigue, anxiety, depression, fear, nurses, healthcare workers,
and healthcare professionals. The selection criteria included: (i)
non-interventional studies on any pandemic outbreaks, (ii)
studies that focused on the impact of any pandemic outbreaks
on the health of healthcare workers, and (iii) studies that iden-
tified various contributing factors of the experiences described
by healthcare workers during any pandemic outbreaks. Articles
that were excluded were those that: (i) focused heavily on clar-
ifying transmission routes and improving surveillance systems,
(ii) emphasized on how the outbreak led to the development of
a particular phenomenon or transition in nursing practice, and
(iii) were conducted on humanitarian aid workers. A total of 31
full-text journal articles were reviewed. The physical and psy-
chological well-being of frontline HCWs was compromised
across all pandemic outbreaks. Many researches evaluated only
the psychological impacts of pandemic outbreaks on frontline
HCWs without considerations of other possible influencing fac-
tors. None reported the mental health statuses of frontline
nurses in particular during the COVID-19 outbreak.

Added value of this study

In the absence of epidemiological data on the mental health of
frontline nurses who are caring for COVID-19 patients and its
associated factors, our study recruited 2014 frontline nurses
with diverse demographic backgrounds and explored their
mental health statuses during the COVID-19 outbreak. There
was a total of 1324 nurses who were originally working in
Wuhan and 690 nurses who were supporting Wuhan from
other provinces in China, making our results a good representa-
tive of the mental health statuses of the Chinese frontlines
nurses woring in Wuhan during the pandemic. We found that
frontline nurses experienced a variety of mental health chal-
lenges, especially burnout and fear. The prevalence of anxiety,
depression, and skin lesion was high. The majority of the nurses
expressed their willingness to participate in frontline work.
Mental health outcomes were positively correlated with skin
lesion and negatively correlated with self-efficacy, resilience,
social support, and frontline work willingness.

Implications of all the available evidence

Future interventions at the organisational and national levels
are needed to improve frontline nurses’ mental health during
the pandemic by addressing its associated factors. Similar
research and support may be extended to include other front-
line healthcare workers.

2 D. Hu et al. / EClinicalMedicine 24 (2020) 100424

HCWs, especially nurses, who come close in contact with these
patients when providing care are often left stricken with inadequate
protections from contamination, high risks of infection, working
burnout, fear, anxiety, and depression [7,8].

Nurses constitute the largest part of the healthcare workforce in
an epidemic [9], and they undertake most of the tasks related to
infectious disease containment [10]. To date, epidemiological data on
the mental health of frontline nurses who are caring for COVID-19
patients and its associated factors are still limited. Such evidence-
based knowledge is crucial for HCWs and the government to prepare
for health responses to pandemics such as COVID-19.

The aim of this study was to examine mental health (burnout,
anxiety, depression, and fear) and its associated factors among front-
line nurses who were caring for COVID-19 patients in Wuhan, China.

The research questions were:

(a) What are the levels of burnout, anxiety, depression, fear, skin
lesion, self-efficacy, resilience, and social support among front-
line nurses?

(b) What are the differences in burnout, anxiety, depression, and
fear between nurses’ various sociodemographic and other
COVID-related background subgroups?

(c) What are the relationships between burnout, anxiety, depres-
sion, fear, and other aforementioned variables?

2. Methods

2.1. Study design

This was a large-scale cross-sectional, descriptive, correlational study.

2.2. Settings and sampling

This study was conducted in two hospitals in Wuhan, China. One
hospital, which consists of three divisions that were located in different
places, was originally a public tertiary hospital in Wuhan, and two out
of the three divisions were converted to venues that only received
COVID-19 patients after 13 January 2020 and 13 February 2020, respec-
tively. These two divisions had 1860 beds in total, with approximately
2000 nurses who were caring for COVID-19 patients. The other hospital
was newly established and operated specially for COVID-19 patients
since 3 February 2020, with 1000 beds and 600 nurses.

All frontline nurses who were caring for COVID-19 patients in the
participating hospitals were invited to participate in this study.
Nurses who were diagnosed with any prior mental disorders and/or
who had the COVID-19 were excluded from the study.

2.3. Outcomes and measurement

Sociodemographic and other COVID-9 related background data
were collected using a self-developed questionnaire. Sociodemo-
graphic data consisted of gender, age, marital status, child-rearing,
monthly household income, education, professional title, clinical
experience, working duration as a frontline nurse, average working
hours per shift, whether Wuhan is the original working place, way to
be dispatched to Wuhan for those nurses from other cities, position
in the hospital, whether the working ward has changed, prior train-
ing or experience of caring similar patients, their confidence in caring
for patients with COVID-19 infection, self-protection, and working
safety. Their belief in their families, colleagues, and hospital readiness
to cope with this COVID-19 outbreak was also collected. Willingness
and reasons to participate in frontline work during the COVID-19 out-
break were also included. Suggestions to improve frontline work
were also explored.

Nurses’ burnout was measured by the Chinese version of the Mas-
lach Burnout Inventory: Human Services Survey (MBI-HSS) for Medi-
cal Personnel (MP) [11], which contains 22 items with three
dimensions: emotional exhaustion (EE, 9 items), depersonalization
(DP, 5 items), and personal accomplishment (PA, 8 items). Each item

D. Hu et al. / EClinicalMedicine 24 (2020) 100424 3

was measured by a seven-point Likert scale. For the EE and DP
dimensions, higher scores meant more severe burnout, while for the
PA dimension, lower scores meant more severe burnout. Scores of
19�26 or �27 on EE, 6�9 or �10 on DP, and 34�39 or �33 on PA
were indicative of moderate or high burnout for the respective
dimensions [11]. The Cronbach’s alpha value of the MBI-HSS for MP
was 0.86 in this study.

Nurses’ anxiety was measured by the Chinese version of Zung’s
Self-Rating Anxiety Scale (SAS) [12]. The SAS contains 20 items that
examine emotional and physical symptoms of anxiety. Each item was
measured by a four-point Likert scale. The total scores ranged from
25 to 100 (20 £ 1 £ 1.25 to 20 £ 4 £ 1.25), with 50�59, 60�69, and
�70 indicating mild, moderate, and severe anxiety, respectively [13].
The Cronbach’s alpha value of the SAS was 0.87 in this study.

Nurses’ depression was measured by the Chinese version of
Zung’s Self-Rating Depression Scale (SDS) [14]. The SDS has 20 items
that assess emotional, physiological, psychomotor, and psychological
imbalance. Each item was measured by a four-point Likert scale. The
total scores ranged from 25 to 100 (20 £ 1 £ 1.25 to 20 £ 4 £ 1.25),
with 53�62, 63�72, and �73 indicating mild, moderate, and severe
depression, respectively [13]. The Cronbach’s alpha value of the SDS
was 0.88 in this study.

Nurses’ fear was measured by the Fear Scale for Healthcare Profes-
sionals (FS-HPs), which was developed by the research team. The FS-
HPs has eight items that assess nurses’ fear of infection and death as
well as nosocomial spreading to their loved ones during COVID-19
outbreak. Each item was measured by a five-point Likert scale. The
total score ranged from 8 to 40, with �19, 20�29, and 30�40 indicat-
ing no or mild fear, moderate, and severe fear, respectively. Ten
experts were invited to evaluate its content validity, giving it a total
Content Validity Index (CVI) of 1.0. The Cronbach’s alpha value of the
FS-HPs was 0.80 in this study.

Skin lesion was measured using a self-developed scale named the
Skin Lesion Scale (SLS) based on the book “Epidemic Prevention Med-
ical Protective Equipment related Skin Lesion and Management”. [15]
The scale has 11 items that examine various common skin lesions
related to personal protective equipment (PPE) among HCWs, includ-
ing facial flushing, blistering of the mouth, skin erosions, skin soak-
ing, skin allergies, skin chapping, skin indentation marks, cutaneous
lichen, red spots with clear boundaries, blisters, and isolated pyo-
derma. For each type of skin lesion, we asked whether each nurse
had such a condition (Each “yes” response was given a score 1 and
each “no” response was given a score of 0, giving a total score of
0�11). For nurses who had skin lesions but could not manage them,
such questions were asked: (1) not sure how to manage them, (2) no
medicine available during the period, and (3) the root cause for the
skin lesions cannot be changed. A group of ten experts were invited
to evaluate the content validity, resulting a total CVI of 1.0. The Cron-
bach’s alpha value of the SLS was 0.73 in this study.

Nurses’ self-efficacy was measured by the Chinese version of the
General Self-efficacy Scale (GSS) [16]. It consists of ten items and
each was measured by a five-point Likert scale. The total score of the
scale ranged from 10 to 40. The higher the score, the better the self-
efficacy. The Cronbach’s alpha value of the GSS was 0.93 in this study.

Nurses’ resilience was measured by the Chinese version of the
Connor-Davidson Resilience Scale-10 (CD-RISC-10) [17]. It contains
ten items with a five-point Likert scale. The total score of the scale
ranged from 0 to 40. The higher the score, the better the resilience.
The Cronbach’s alpha value of the CD-RISC-10 was 0.96 in this study.

Social support was measured using the Chinese version of the
Multidimensional Scale of Perceived Social Support (MSPSS) [18].
The scale consists of 12 items and uses a seven-point Likert scale. It
has two subscales: intra-family social support and extra-family
social support. The higher the mean score, the better the social
support. The Cronbach’s alpha value of the MSPSS was 0.96 in this
study.

2.4. Data collection procedure

The online questionnaire survey was developed using an online
platform called “Questionnaire Star”. After obtaining ethical approval
from the two participating hospitals, the directors of nursing and the
head nurses were informed about the inclusion and exclusion crite-
ria. The head nurses distributed the online survey to the WeChat
group of frontline nurses who were caring for COVID-19 patients on
13 February 2020. Those who had interest in the survey then filled in
the survey on the “Questionnaire Star” platform, which had a feature
that only when all questions were answered, the online question-
naire could be submitted. A token of appreciation of 50 RMB (equiva-
lent to 7 USD) was provided to each participant via the WeChat red
packet on the completion of the online survey. Data collection was
completed on 24 February 2020. The study protocol has been pub-
lished on the last author’s institutional website.

2.5. Ethical considerations

Ethical approval was obtained from the participating hospitals’
ethical review boards as well as the last author’s university. All nurses
provided consent by ticking the “yes” box to indicate their willing-
ness to participate in the online survey. Voluntary participation and
data confidentiality were emphasized.

2.6. Data analyses

Data were analysed using IBM SPSS version 25.0 for Windows
[19]. Descriptive statistics were used to summarize nurses’ sociode-
mographic and other COVID-related background variable subgroups
(such as working duration as the frontline nurses, reasons for being
dispatched to Wuhan, confidence in self-protection, and so on) and
all continuous outcome variables (including burnout, fear, anxiety,
depression, fear, skin lesion, self-efficacy, resilience, and social sup-
port). An independent two-sample t-test was used to examine the
differences in mental health outcomes between sociodemographic
and other COVID-related background variable subgroups. Pearson
product-moment correlation coefficient was used to examine the
relationships between burnout, fear, anxiety, and depression and all
other continuous outcome variables. P values of less than 0.05 were
considered statistically significant.

2.7. Role of funding source

The funding bodies had no role in study design, data collection,
analysis, and interpretation, the manuscript writing, or submission
decision. The corresponding authors had full access to all the data
and had final responsibility for the decision to submit for publication.

3. Results

3.1. Sociodemographic and other characteristics of the participants

Of the 2110 nurses who opened the survey link, nine (0.4%) ticked
the “no” box to indicate their unwillingness to participate in the
study and withdrew from the survey. Among the rest of 2101 nurses
who completed and submitted the survey, 68 (3.2%) nurses reported
that the number of days working at the frontline was zero indicating
they had not begun their duties as frontline nurses, and 19 (0.9%)
spent less than five minutes to complete the survey with several
scales ticking the same answers consecutively (Fig. 1). Thus, these
nurses were excluded, leaving a total of 2014 frontline nurses who
were included in this study.

Table 1 shows the participants’ sociodemographic and other char-
acteristics. The mean age of the frontline nurses was 30.99 (SD=6.17)
years old. The mean working duration as frontline nurses was 20.72

E
nr
ol
m
en
t

A
na
ly
si
s

Excluded: (n=348)
Reasons:
� Not opened the

survey link (n=348)

Opened the survey link at WUH
(n=1652)

Data analysis (n=2014, including 1578 from WUH, 436 from HSST)

Invited to participate at WUH
(n=2000)

Invited to participate at HSST
(n=600)

Excluded: (n=142)
Reasons:
� Not opened the

survey link (n=142)

Opened the survey link at HSST
(n=458)

Excluded: (n=2)
Reasons:
� Ticked the “no” box

indicating
unwillingness of
participation (n=2)

Excluded: (n=67)
Reasons:
� Had not begun their

duty as frontline
nurses (n=52)

� Invalid questionnaires
(n=15)

Excluded: (n=7)
Reasons:
� Ticked the “no” box

indicating
unwillingness of
participation (n=7)

Excluded: (n=20)
Reasons:
� Had not begun their

duty as frontline nurses
(n=16)

� Invalid questionnaires
(n=4)

Completed and submitted the survey
at WUH (n=1645)

Completed and submitted the survey
at HSST (n=456)

Fig. 1. Flowchart of recruitment process.
Note: Abbreviation: WUH, Wuhan Union Hospital, Huazhong University of Science and Technology; HSSH, Huo Shen Shan hospital.

4 D. Hu et al. / EClinicalMedicine 24 (2020) 100424

(SD=12.9) days, and the average working hours was 6.57 (SD=1.90)
hours per shift. The majority of the frontline nurses were female
(87.1%), were married (61.1%), had one or more children (54.6%), had
bachelor’s degrees or higher (78.1%), and had junior professional
titles (74.2%). There were a total of 1324 nurses who originally
worked in Wuhan and 690 nurses who were sent to support Wuhan
from other provinces in China. Among these 690 nurses, 476 were
voluntary and 214 (209 willing and 5 unwilling) were delegated by
their hospitals. The majority of the participants (n = 1, 654, 82.1%)
received prior training, but 1229 (61.0%) participants had no prior
experiences of caring for patients with infectious diseases. A large
number of frontline nurses had confidence in caring for COVID-19
patients, self-protection, and work safety. The majority of the front-
line nurses believed that their family, colleagues, and hospitals were
ready to cope with the COVID-19 outbreak.

The majority of the participants (n = 1950, 96.8%) indicated their
willingness to participate in frontline work with the following rea-
sons: responsibility and mission as a nurse, prior experiences during
the SARS outbreak, patriotism, dedication, helping others, extra wel-
fare, hospital assignment, and the mission as a communist party
member. Some participants (n = 64, 3.2%) indicated their unwilling-
ness because of safety concerns, family caring needs such as breast-
feeding, fear, work stress, and personal health problems.

The participants put forward some suggestions to support front-
line nurses’ work: (1) improve the welfare and social statuses of
frontline nurses, (2) strengthen training regarding self-protection
and provide adequate PPE, (3) enhance manpower and resource allo-
cations, (4) improve the conditions of accommodation, food, and
environments for frontline nurses, and (5) offer more psychosocial
support to frontline nurses.

3.2. Participants’ mental health and other outcomes

Table 2 shows the mental health and other outcomes of the front-
line nurses. The participants had moderate levels of burnout, as
shown in EE (mean=23.44, SD=13.80), DP (mean=6.77,SD=7.05), and
PA (mean=34.83, SD= 9.95). The participants reported high levels of
fear (mean=30.41, SD=7.60).

Eight hundred and thirty-five (41.5%) nurses reported high EE,
556 (27.6%) nurses indicated high DP, and 771 (38.3%) had no or low
PA, which all indicated high burnout during work. The participants
reported mild (n = 545, 27.1%), moderate (n = 221, 11.0%), and severe
(n = 67, 3.3%) anxiety. Similarly, the participants indicated mild
(n = 661, 32.8%), moderate (n = 194, 9.6%), and severe (n = 23, 1.1%)
depression. The majority of the nurses reported moderate (n = 564,
28%) and high (n = 1273, 36.2%) fear.

Table 1
Sociodemographic and other characteristics of the frontline nurses (n = 2014).

Sociodemographic variables Mean (SD) n (%)

Gender
Male 260 (12.9%)
Female 1754 (87.1%)

Age (years): mean (SD) 30.99 (6.17)
Marital status
Married 1230 (61.1%)
Other marital statusy 784 (38.9%)

Had one or more children
Yes 1100 (54.6%)
No 914 (45.4%)

Monthly household income (USD/month)
�1440 1109 (55.1%)
>1440 905 (44.9%)

Education
Diploma or lower 441 (21.9%)
Bachelor’s degree or higher 1573 (78.1%)

Professional title
Junior 1495 (74.2%)
Intermediate and senior 519 (25.8%)

Clinical experience (months) 107.76 (78.09)
Working duration as frontline nurse during
the COVID-19 outbreak (days)

20.72 (12.94)

Average working hours/shift 6.57 (1.90)
Wuhan as original working place
Yes 1324 (65.7%)
No 690 (34.3%)

Reasons for being dispatched to Wuhan
(n = 690)
Delegated by the hospital, willingly or
unwillingly

214 (31.0%)

Voluntary 476 (69.0%)
Position in original hospital
Bedside nurse 1818 (90.3%)
Head nurse or nurse director (including
vice-director)

196 (9.7%)

Position in the hospital at Wuhan
Bedside nurse 1894 (94.0%)
Head nurse or nurse director (including
vice-director)

120 (6.0%)

Working wards changed
Yes 747 (37.1%)
No 1267 (62.9%)

Prior training about caring patients with
infectious diseases
Yes 1654 (82.1%)
No 360 (17.9%)

Prior experience of caring patients with
infectious diseases
Yes 785 (39.0%)
No 1229 (61.0%)

Confidence in caring COVID-19 patientsa

Unconfident 796 (39.5%)
Confident 1218 (60.5%)

Confidence in self-protectiona

Unconfident 863 (42.9%)
Confident 1151 (57.1%)

Evaluation of work safety while caring
COVID-19 patientsb

Unsafe 844 (41.9%)
Safe 1170 (58.1%)

Belief in your family’s readiness to cope with
this COVID-19 outbreak
Not believe 586 (29.1%)
Believe 1428 (70.9%)

Belief in your colleagues’ readiness to cope
with this COVID-19 outbreak
Not believe 413 (20.5%)
Believe 1601 (79.5%)

Belief in your hospital’s readiness to cope
with this COVID-19 outbreak
Not believe 361 (17.9%)
Believe 1653 (82.1%)

Willingness to participate in frontline work
during the COVID-19 outbreak

(continued)

Table 1 (Continued)

Sociodemographic variables Mean (SD) n (%)

Yes 1950 (96.8%)
No 64 (3.2%)

y Including single, divorced, or separated.
a Measured by a 5-point scale and regrouped into two categories: Unconfident,

including “1=Very unconfident”, “2=Unconfident”, and “3=Somewhat confident”,
and Confident, including “4=Confident” and “5=Very confident”.

b Measured by a 5-point scale and regrouped into two categories: Unsafe,
including “1=Very unsafe”, “2=Unsafe”, and “3=Somewhat Safe”, and Safe, including
“4=Safe” and “5=Very safe”.

D. Hu et al. / EClinicalMedicine 24 (2020) 100424 5

The majority of the participants (n = 1910, 94.8%) had one or more
skin lesion(s) caused by PPE. Among nurses who did not manage their
skin lesions (n = 1703, 84.6%), 316 nurses (15.7%) indicated that they
were not sure about the management, 518 nurses (25.7%) indicated
that no medicine was available during the period, and 718 nurses
(35.7%) said that the root causes were not changeable. Besides the 11
skin lesions that we included in our self-developed scale, some
nurses mentioned other skin lesions such as conjunctivitis, ear ten-
derness, decrustation, beriberi, and needle stick injuries.

3.3. Differences in mental health outcome levels between various
sociodemographic and other characteristic subgroups for the
participants

Table 3 shows the differences in the burnout, anxiety, depression,
and fear levels between various sociodemographic and other charac-
teristic subgroups. It was typical for one mental health variable to
have significant differences for some, but not all sociodemographic
and other characteristic subgroups. However, statistically significant
differences in the levels of burnout, anxiety, depression, and fear
were found between subgroups of the following variables: profes-
sional title (p<0.05), whether Wuhan was the original working place
(p<0.05), whether working wards had changed (p<0.05), confidence
in caring for COVID-19 patients (p<0.001), confidence in self-protec-
tion (p<0.001), evaluations of work safety (p<0.001), belief in fam-
ily’s or colleagues’ or hospitals’ readiness to cope with the COVID-19
outbreak (p<0.001), and willingness to participate frontline work
(p<0.01) .

3.4. Relationships among mental health and other health outcomes

Table 4 showed the relationships among mental health and other
health outcomes for frontline nurses. EE was positively correlated
with skin lesion (r = 0.182) and negatively correlated with self-effi-
cacy (r=�0.193), resilience (r=�0.325), intra-family social support
(r=�0.170), and extra-family social support (r=�0.234). DP was nega-
tively correlated with resilience (r=�0.208), intra-family social sup-
port (r=�0.221), and extra-family social support (r=�0.216). PA was
positively correlated with self-efficacy (r = 0.376), resilience
(r = 0.436), intra-family social support (r = 0.348), and extra-family
social support (r = 0.363). Anxiety was positively correlated with skin
lesion (r = 0.265) and negatively correlated with self-efficacy
(r=�0.262), resilience (r=�0.427), intra-family social support
(r=�0.274), and extra-family social support (r=�0.333). Similarly,
depression was positively correlated with skin lesion (r = 0.224) and
negatively correlated with self-efficacy(r=�0.409), resilience
(r=�0.554), intra-family social support (r=�0.384), and extra-family
social support (r=�0.455). Fear was negatively correlated with resil-
ience (r=�0.121).

Table 2
Health outcomes of the frontline nurses (n = 2014).

Mental health variables Mean (SD) n (%) Possible range

Burnout (MBI-HSS)a: Emotional exhaustion 23.44 (13.80) 0 to 54
No or mild emotional exhaustion (�18) 796 (39.5%)
Moderate emotional exhaustion (19�26) 383 (19.0%)
High emotional exhaustion: (�27) 835 (41.5%)

Burnout (MBI-HSS)a: depersonalization 6.77 (7.05) 0 to 30
No or mild depersonalization (�5) 1161 (57.6%)
Moderate depersonalization (6�9) 297 (14.7%)
High depersonalization: (�10) 556 (27.6%)

Burnout (MBI-HSS)a: personal accomplishment 34.83 (9.95) 0 to 48
High personal accomplishment indicating low burnout (�40) 795 (39.5%)
Moderate personal accomplishment indicating moderate burnout (34�39) 448 (22.2%)
No or mild personal accomplishment indicating high burnout (�33) 771 (38.3%)

Anxiety (SAS)b 47.80 (11.20) 25 to 100
No anxiety (<50) 1181 (58.6%)
Mild anxiety (50�59) 545 (27.1%)
Moderate anxiety (60�69) 221 (11.0%)
Severe anxiety (�70) 67 (3.3%)

Depression (SDS)c 50.50 (11.31) 25 to 100
No depression (<53) 1136 (56.4%)
Mild depression (53�62) 661 (32.8%)
Moderate depression (63�72) 194 (9.6%)
Severe depression (�73) 23 (1.1%)

Fear (FS-HPs)d 30.41 (7.60) 8 to 40
No or mild fear (�19) 177(8.3%)
Moderate fear (19�29) 564 (28.0%)
Severe fear (30�40) 1273 (63.2%)

Skin lesion (SLS)e 3.91 (2.30) 0

Statistics homework help

Data

Percent
Under 21
Fatal Accidents
per 1000
13 2.962
12 0.708
8 0.885
12 1.652
11 2.091
17 2.627
18 3.83
8 0.368
13 1.142
8 0.645
9 1.028
16 2.801
12 1.405
9 1.433
10 0.039
9 0.338
11 1.849
12 2.246
14 2.855
14 2.352
11 1.294
17 4.1
8 2.19
16 3.623
15 2.623
9 0.835
8 0.82
14 2.89
8 1.267
15 3.224
10 1.014
10 0.493
14 1.443
18 3.614
10 1.926
14 1.643
16 2.943
12 1.913
15 2.814
13 2.634
9 0.926
17 3.256

Sheet2

Sheet3

Statistics homework help

SPECIAL ISSUE

Workplace stress and resilience in the Australian
nursing workforce: A comprehensive integrative
review

Eric Badu,1 Anthony Paul O’Brien,2 Rebecca Mitchell,3 Mark Rubin,4 Carole James,5

Karen McNeil,6 Kim Nguyen7 and Michelle Giles7
1School of Nursing and Midwifery, 2Faculty Health and Medicine, School Nursing and Midwifery, The University of
Newcastle Australia, Callaghan, 3Faculty of Business and Economics, Macquarie University, Sydney, 4School of
Psychology, 5Faculty of Health and Medicine, 6Faculty of Business and Law, The University of Newcastle, Australia,
Callaghan, and 7Hunter New England Local Health District, Newcastle, New South Wales, Australia

ABSTRACT: This integrative review aimed to identify and synthesize evidence on workplace
stress and resilience in the Australian nursing workforce. A search of the published literature was
conducted using EMBASE, MEDLINE, CINAHL (EBSCO), PsycINFO, Web of Science, and
Scopus. The search was limited to papers published in English from January 2008 to December
2018. The review integrated both qualitative and quantitative data into a single synthesis. Of the
41 papers that met the inclusion criteria, 65.85% (27/41) used quantitative data, 29.26% (12/41)
used qualitative data, and 4.87% (2/41) used mixed methods. About 48.78% (20/41) of the papers
addressed resilience issues, 46.34% (19/41) addressed workplace stress, and 4.87% (2/41)
addressed both workplace stress and resilience. The synthesis indicated that nurses experience
moderate to high levels of stress. Several individual attributes and organizational resources are
employed by nurses to manage workplace adversity. The individual attributes include the use of
work–life balance and organizing work as a mindful strategy, as well as self-reliance, passion and
interest, positive thinking, and emotional intelligence as self-efficacy mechanisms. The
organizational resources used to build resilience are support services (both formal and informal),
leadership, and role modelling. The empirical studies on resilience largely address individual
attributes and organizational resources used to build resilience, with relatively few studies
focusing on workplace interventions. Our review recommends that research attention be devoted
to educational interventions to achieve sustainable improvements in the mental health and
wellbeing of nurses.

KEY WORDS: Australia, coping strategies, mental health nursing, resilience, stress, workplace.

INTRODUCTION

Resilience has historically been defined and measured
using several theoretical and conceptual approaches
(Aburn et al., 2016; Delgado et al., 2017). Resilience is
a dynamic and adaptable concept, especially in the
context of overcoming adversity within the parameters
of the individual developmental and transformative
continuum (Aburn et al., 2016; Scoloveno, 2016). In
addition, resilience is defined as the ability to bounce
back, overcome adversity, adapt, and adjust, as well as

Correspondence: Eric Badu, School of Nursing and Midwifery,
The University of Newcastle (UON), University Drive, Callaghan,
NSW 2308, Australia. Email: eric.badu@uon.edu.au
Declaration of conflict of interest: The authors declare that
there is no conflicts of interest.

Eric Badu, BA, MSc.
Anthony Paul O’Brien, BA, MA, PhD.
Rebecca Mitchell, MBS, PhD.
Mark Rubin, BSc, MSc, PhD.
Carole James, BSc, MSc, PhD.
Karen McNeil, MBA, PhD.
Kim Nguyen, GradDipPH, GradDipStratLDRSHP, DipHRMgt,
BAppSc(OT).
Michelle Giles, RN, CM, BBus MIS, PhD.

Accepted August 28 2019.

© 2019 Australian College of Mental Health Nurses Inc.

International Journal of Mental Health Nursing (2020) 29, 5–34 doi: 10.1111/inm.12662

bs_bs_banner

maintain good mental health (Aburn et al., 2016; Ear-
volino-Ramirez, 2007; Garcia-Dia et al., 2013). Specifi-
cally, Scoloveno (2016, p. 3) described resilience as
‘the ability of individuals, families and groups to suc-
cessfully function and adapt and cope in spite of psy-
chological, sociological, cultural and/or physical
adversity’.

During past decades, considerable global attention
has been drawn to resilience employed to mitigate the
negative effects of workplace stress and to prevent
poor psychosocial outcomes among nurses (Delgado
et al., 2017; Garcia-Dia et al., 2013; Turner, 2014).
Several studies have identified significant outcomes or
consequences of resilience. The outcomes are largely
related to effective coping, mastery of positive adapta-
tion (Earvolino-Ramirez, 2007; Garcia-Dia et al.,
2013), sound mind and body, personal control, psycho-
logical adjustment, and personal growth (Garcia-Dia
et al., 2013). Specifically, some studies have recom-
mended that resilience is not only significant for
enhancing the psychological wellbeing of individual
nurses, but also for improving mental health service
delivery – particularly in ensuring the longevity and
retention of the nursing workforce (Kim & Windsor,
2015; Turner, 2014).

Consequently, several studies have developed theo-
retical models to facilitate understandings of resilience
among workplace nurses (e.g., nurses working in
health facility setting; Cusack et al., 2016; Earvolino-
Ramirez, 2007; Garcia-Dia et al., 2013; Rees et al.,
2015; Scoloveno, 2016; Turner, 2014; Zander & Hut-
ton, 2009). The theoretical models have been
explained according to different interrelated subcon-
structs. Generally, the predicting or protective factors
used to build resilience in workplace nursing can be
categorized according to individual attributes, organiza-
tional (e.g., workplace factors), and external factors
(Garcia-Dia et al., 2013; Kim & Windsor, 2015; Scolo-
veno, 2016; Yılmaz, 2017). Individual, organizational,
and external factors can individually or jointly con-
tribute to building resilience among workplace nurses.
The individual characteristics, which appear as internal
factors, are personality traits, cognitive ability, neuro-
plasticity, self-efficacy (self-help skills) (Garcia-Dia
et al., 2013; Rees et al., 2015), optimism and hope
(Scoloveno, 2016), a sense of humour, mindfulness
(control), competence, spirituality, adaptability, and a
positive identity (Rees et al., 2015; Yılmaz, 2017).
Conversely, the organizational factors are mostly
characterized by professional skills development, social
support, a supportive workplace environment, work

programmes (bio-psychosocial health programmes),
and interventions implemented by workplace organiza-
tions (Delgado et al., 2017; Scoloveno, 2016; Yılmaz,
2017). In addition, Yılmaz (2017) recommended that
professional attributes associated with cultural generali-
ties – such as altruism, mentoring, setting a good
example, coaching, leading, and motivating – can be
encouraged among the nursing profession to facilitate
resilience. Some studies have indicated that external
factors – including family, community, and socioeco-
nomic resources – can contribute to building resilience
in the nursing workforce (Garcia-Dia et al., 2013; Kim
& Windsor, 2015).

In Australia, there is growing evidence regarding the
effect of stress among workplace nurses. The stressors
may be caused by several factors, including organiza-
tional and individual factors. Consequently, resilience
seems important for nurses, as their organizational
environment includes stressors that contribute to psy-
chological distress. Resilience and its associated coping
strategies may be employed to mitigate the workplace
stress faced by nurses. This issue has resulted in grow-
ing empirical studies on resilience employed to manage
workplace stress. However, only a few studies have
attempted to synthesize evidence on the concept. A
preliminary search as part of this integrative review
identified two papers that sought to synthesize evi-
dence on stress and coping mechanisms, as well as
models of resilience, among Australian workplace
nurses (Lim, Bogossian, & Ahern, 2010; Zander &
Hutton, 2009). Of these two studies, one aimed to
identify the factors that contribute to stress, the effects
of stress on health and wellbeing, and coping strategies
to manage stress (Lim et al., 2010), while the other
study addressed stress, yet was limited to oncology
nurses (Zander & Hutton, 2009). Critically, no study
has been undertaken to aggregate a synthesis of both
qualitative and quantitative studies regarding resilience
displayed by Australian nurses at work.

As such, this study aims to contribute to the
research lacuna by conducting an integrative review
into the level of stress and the resilience developed by
Australian nurses to reduce workplace adversity. The
study specifically aims to identify the levels of stress
and synthesize evidence on the individual attributes
and organizational resources used to build resilience.

The review findings are significant for several rea-
sons. The evidence is expected to inform policy deci-
sion-making on the wellbeing of the nursing
workforce and to strengthen human resource manage-
ment for health. The evidence is also considered to

© 2019 Australian College of Mental Health Nurses Inc.

6 E. BADU ET AL.

be valuable to policy makers and managers in pre-
venting stress and burnout in the nursing workforce.
Finally, the evidence can guide researchers and clini-
cians with regard to directions for future research
into building resilience among nurses and student
nurses.

METHODS

Methodology

The methodology used for this integrative review was
conducted according to Whittemore and Knafl (2005).
An integrative review is an approach that allows simul-
taneous inclusion of diverse methodologies (i.e., experi-
mental and nonexperimental research) and varied
perspectives to fully understand the phenomenon of
concern (Hopia et al., 2016; Whittemore & Knafl,
2005). The integrative review methods aim to use
diverse data sources to develop a holistic understanding
of resilience in nursing. This review method can con-
tribute greatly to evidence-based practice for nursing.
The methodology involves five stages:

• problem identification (ensuring that the research
question and purpose are clearly defined)

• literature search (incorporating a comprehensive
search strategy)

• data evaluation (focusing methodological quality)
• data analysis (data reduction, display, comparison,
and conclusions)

• presentation (synthesizing findings in a model or the-
ory, and describing the implications for practice, pol-
icy, and research; Whittemore & Knafl, 2005).

Inclusion criteria

The integrative review included papers that used a
qualitative, quantitative, or mixed-methods approach.
The quantitative papers targeted studies that used
quantitative randomized controlled trials, quantitative
nonrandomized designs (analytical cross-sectional), and
quantitative descriptive studies. The qualitative papers
broadly used phenomenological, grounded theory, nar-
rative, ethnography, and participatory methodology.
The integrative review included papers that targeted all
resilience issues in nursing workforce, papers that
assessed workplace stress among nurses, and papers
that examined the effect of resilience in mitigating
workplace adversity. The included articles were limited
to those that targeted Australian nurses.

Exclusion criteria

The review excluded papers that did not address resili-
ence in nursing; that targeted resilience in organiza-
tions outside a nursing environment; and that focused
on nursing students, nurses in an education setting, or
new graduates and nursing managers. Nurses working
in these environments were excluded because their
experience regarding stress and resilience may differ
from nurses in the hospital setting. Other general
exclusion criteria were conference abstracts, papers
that present opinion, book chapters, editorials, com-
mentaries, clinical case, and review studies. The review
also excluded papers published prior to 2008, as well
as non-English-language articles.

Search strategy

The integrative review included all peer-reviewed pub-
lished articles addressing resilience and the coping
strategies used to manage stress among workplace
nurses in Australia. The searches of published articles
were conducted from six electronic databases:
EMBASE, CINAHL (EBSCO), Web of Science, Sco-
pus, PsycINFO, and MEDLINE. The searches of pub-
lished articles were conducted according to the Joanna
Briggs Institute (JBI) recommended guidelines for con-
ducting systematic reviews (Pearson et al., 2014). In
particular, a three-step search strategy was used to con-
duct the search for information. An initial limited
search of MEDLINE and EMBASE was conducted,
followed by analysis of the text contained in the title
and abstract, and of the index terms used to describe
the article (Pearson et al., 2014). A second search using
all identified keywords and index terms was then con-
ducted across all remaining five databases. Finally, the
reference lists of all identified articles were hand-
searched for additional studies (Pearson et al., 2014).
The review considered only studies published in the
English language. Studies published from January 2008
to December 2018 were considered for inclusion in
this review.

Search terms and Boolean operators

This study used the following search terms:
(‘nurses’ OR ‘nurse resilience*’ OR ‘workplace resili-

ence’ OR ‘team resilience’ OR ‘team effectiveness’ OR
‘employee resilience’ OR ‘organizational resilience’ OR
‘resilience’ or ‘psychological’) AND (‘wellbeing’ OR
‘adaptation’ OR ‘coping behavior’ OR ‘job satisfaction’

© 2019 Australian College of Mental Health Nurses Inc.

RESILIENCE IN WORKPLACE NURSING 7

OR ‘job performance’ OR ‘job satisfaction’) AND
(‘stress management’ or ‘stress’ or ‘nurse workplace
stress’ OR ‘burnout’ OR ‘professional’ OR ‘workplace’
or ‘workplace stress’ OR ‘occupational stress’ OR ‘de-
pression’ OR ‘anxiety’).

Selection process

The review used several stages to manage the selection
of included articles (Pearson et al., 2014). Two authors
independently screened the titles of articles and then
approved those that met the selection criteria. All
authors reviewed the abstracts and agreed on those
that needed full-text screening. Additionally, the
authors screened all full-text articles and confirmed
that the information and records met the inclusion cri-
teria. All authors used the Preferred Reporting Items
for Systematic Reviews and Meta-Analyses (PRISMA)
flowchart for systematic reviews (Moher et al., 2009) to
represent the selection processes (see Fig. 1).

Data management and extraction

Two reviewers independently managed the data
extraction process. Endnote X8 software was used to
manage the search results, screening, review of arti-
cles, and removal of duplicate references. The authors
developed a data extraction form to handle all aspects
of data extraction (Appendix 1). The data extraction
form was developed according to Cochrane and the
JBI manuals (Pearson et al., 2014) for conducting sys-
tematic reviews, as well as consultation with experts in
methodologies and the subject area. The authors
extracted the results of the included papers in numeri-
cal, tabular, and textual format (Pearson et al., 2014).
Categories that were extracted included the study
details (citation, year of publication, author, contact
details of lead author, and funder/sponsoring organiza-
tion), publication source, methodological characteris-
tics, study population, subject area (e.g., nurses’
workplace stress, effect of nurses’ workplace stress,

Records identified through database
searching
(n = 406)

Duplicates records removed
(n =83)

Records after duplicates removed
(n = 323)

Records screened
(n = 323)

Records excluded
(n = 266)

Full-text articles assessed
for eligibility

(n = 57)

Full-text articles excluded, with
reasons (n = 17)

• Reviews (n = 6)
• Home and Community

Care workers (n = 1)
• Focused on other

settings (Singapore and
Iran, China, UK) (n = 4)

• Protocol (n = 1)
• Not focusing on

resilience (n = 4)
• No full text available

(n = 1)

Studies included in
quantitative and

Qualitative synthesis
(n = 41)

Full text articles
included from
reference list

(n = 1)

Sc
re

en
in

g
In

cl
ud

ed
El

ig
ib

ili
ty

Id
en

tif
ic

at
io

n

FIG. 1: legend: Flow chart of included papers. [Colour figure can be viewed at wileyonlinelibrary.com]

© 2019 Australian College of Mental Health Nurses Inc.

8 E. BADU ET AL.

concept of resilience, antecedents to resilience, and
effect of resilience on workplace nurses’ stress), exist-
ing interventions and outcomes, additional information
on resilience, recommendations, and other potential
references to follow up.

Assessment of methodological quality

The methodological quality of all included papers was
independently assessed or appraised by two reviewers.
The authors also developed a critical appraisal check-
list using the Mixed Methods Appraisal Tool (Hong
et al., 2018) and JBI (2017) critical appraisal tool.
The critical appraisal tool was subdivided into sec-
tions. The sections included reviewers’ details, study
details (methods, study design, data, and analysis),
screening questions (categorized according to qualita-
tive, quantitative randomized controlled, and quantita-
tive non-randomized trials, including cohort study,
case-control study, analytical cross-sectional study,
quantitative descriptive study, systematic review, and
mixed-methods study), and overall quality score. Each
of the subsections had specific questions related to
methodological and reporting quality (Appendix 2).
The appraisal was conducted to assess the method-
ological quality of the included papers and to further
determine whether to include or exclude articles, or
to seek further information from authors. The
methodological quality scores were categorized into
low quality (a score below 25%), medium quality (a
score of 50%), and high quality (a score of 70% or
above). The scores were computed by summing the
number of ‘yes’ occasions for each subsection of the
questions related to the methodological criteria, and
further expressing them as a percentage (Hong et al.,
2018).

Data synthesis

The extracted data were analysed using a mixed-meth-
ods synthesis (Pearson et al., 2014; Whittemore &
Knafl, 2005). The authors coded the quantitative and
qualitative data together. Data display matrices were
developed to document all the coded ideas from the
extracted data (Whittemore & Knafl, 2005). Alphabets
and colours were assigned to each of the coded ideas.
The resulting codes from quantitative and qualitative
data were used to generate a descriptive themes (Pear-
son et al., 2014). The themes were consistent with the
various concepts and theoretical constructs that facili-
tate resilience in workplace – namely, individual

(personal characteristics), organizational (workplace or
environmental), and external factors (Cusack et al.,
2016; Earvolino-Ramirez, 2007; Garcia-Dia et al., 2013;
Rees et al., 2015; Scoloveno, 2016; Turner, 2014; Zan-
der & Hutton, 2009). The background information of
the included papers and emerging codes were analysed
using STATA version 15.

RESULTS

Description of retrieved papers

The study identified 406 papers from all databases
searched, after which 83 duplicate records were
deleted. Of the nonduplicate records, 323 papers were
screened for eligibility, after which 266 were excluded.
After data extraction of 57 full-text articles and
methodological quality assessment, one paper was iden-
tified from the reference list, and 17 papers were
excluded. Overall, 41 papers were included in the final
synthesis (see Fig. 1). Of the 41 papers, 40 met the cri-
teria for high methodological quality assessment, while
only one paper had medium quality (see Table 1).

Characteristics of included papers

Most of the included papers reported the study design
that was used, while 29.26% (12/41) did not report the
study design. Of the papers reporting a study design,
more than one-third (12/29; 41.37%) used cross-sec-
tional design, 17.24 (5/29) used interpretive phe-
nomenological approaches, and 10.34 (3/29) used case
studies (see Table 1). Most of the included papers used
quantitative data (27/41; 65.85), while 29.26% (12/41)
used qualitative data and 4.87% (2/41) used mixed
methods. More than one-third of the included papers
(20/41; 48.78%) addressed resilience issues, while
46.34% (19/41) addressed stress, and 4.87% (2/41)
addressed both stress and resilience. Most of the
included papers employed several validated instru-
ments, while a few used qualitative data collection
approaches, such as in-depth interviews, focus group
discussions, and workshops (see Table 1). Most of the
included papers (25/41; 60.97%) recruited both males
and females, while more than one-third (12/29;
41.37%) targeted only females. The majority of
included papers (25/41; 60.97%) analysed the results
using descriptive and inferential statistics, while
26.82% (11/41) used thematic analysis, 4.87% used
descriptive statistics, and 4.87% used concurrent analy-
sis (see Table 1).

© 2019 Australian College of Mental Health Nurses Inc.

RESILIENCE IN WORKPLACE NURSING 9

T
A
B
L
E

1
:
C
h
ar
ac
te
ri
st
ic
s
of

in
cl
u
d
ed

ar
ti
cl
es

In
cl
u
d
e
d

ar
ti
cl
e

O
b
je
ct
iv
e
s

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ar
g
e
t

G
e
n
d
e
r

S
tu
d
y
d
e
si
g
n

M
e
th
o
d
s

D
at
a
co
ll
e
ct
io
n
in
st
ru
m
e
n
t

A
n
al
ys
is

Q
u
al
it
y

sc
o
re

A
b
ra
h
am

et
al
.

(2
0
1
8
)

T
o
d
e
sc
ri
b
e
th
e
E
D

w
o
rk
in
g

e
n
vi
ro
n
m
e
n
t
as

p
e
rc
e
iv
e
d
b
y

m
e
d
ic
al

an
d
n
u
rs
in
g
st
af
f

w
o
rk
in
g
in

tw
o
d
if
fe
re
n
t-
si
ze
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E
D
s
w
it
h
in

th
e
sa
m
e

h
e
al
th
ca
re

se
rv
ic
e
.

W
o
rk
p
la
ce

st
re
ss

F
e
m
al
e
s

an
d

m
al
e
s

C
ro
ss
-s
e
ct
io
n
al

Q
u
an
ti
ta
ti
ve


W
o
rk
in
g
E
n
vi
ro
n
m
e
n
t

S
ca
le
-1
0
(W

E
S
-1
0
);


T
h
e
Ja
lo
w
ie
c
C
o
p
in
g

S
ca
le

p
ar
t
A
(J
C
S
-A
);


w
o
rk
p
la
ce

st
re
ss
o
rs

D
e
sc
ri
p
ti
ve

st
at
is
ti
cs

H
ig
h

A
ll
e
n
et

al
.

(2
0
1
5
)

T
o
e
xa
m
in
e
th
e
re
la
ti
o
n
sh
ip

b
e
tw
e
e
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b
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ll
yi
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g
an
d
b
u
rn
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t

an
d
th
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p
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ti
al

b
u
ff
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ri
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ff
e
ct

p
sy
ch
o
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g
ic
al

d
e
ta
ch
m
e
n
t

m
ig
h
t
h
av
e
o
n
th
is
re
la
ti
o
n
sh
ip
.

W
o
rk
p
la
ce

st
re
ss

F
e
m
al
e
s

an
d

m
al
e
s

C
ro
ss
-s
e
ct
io
n
al

Q
u
an
ti
ta
ti
ve


S
ca
le

d
e
ve
lo
p
e
d
b
y

Q
u
in
e
;


R
e
co
ve
ry

E
xp
e
ri
e
n
ce

Q
u
e
st
io
n
n
ai
re
;


C
o
p
e
n
h
ag
e
n

B
u
rn
o
u
t
In
ve
n
to
ry

(C
B
I)

D
e
sc
ri
p
ti
ve

an
d
in
fe
re
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ti
al

H
ig
h

B
o
w
d
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n
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al
.

(2
0
1
5
)

T
o
e
xa
m
in
e
d
so
u
rc
e
s
o
f
w
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re
la
te
d
st
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an
d
re
w
ar
d

sp
e
ci
fi
c
to

m
u
lt
id
is
ci
p
li
n
ar
y

st
af
f
w
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rk
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g
in

p
ae
d
ia
tr
ic

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n
co
lo
g
y
in

A
u
st
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li
a.

W
o
rk
p
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st
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F
e
m
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an
d

m
al
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N
o
t
re
p
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rt
e
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Q
u
an
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ti
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W
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rk

st
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sc
al
e

p
ae
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n
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d
in
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ro
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B
ro
w
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(2
0
1
0
)

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id
e
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th
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fa
ct
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th
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im
p
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t
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o
f

re
g
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te
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d
ag
e
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n
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rs
e
s,

th
at

is
th
e
ir
ca
p
ac
it
y
to

ad
ap
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to

th
e
p
h
ys
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,
m
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l
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d

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d
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d
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fa
ci
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ce

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m
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s

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te
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p
h
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m
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al

Q
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ti
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-d
e
p
th

in
te
rv
ie
w
s

T
h
e
m
at
ic

an
al
ys
is

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ig
h

C
o
p
e
et

al
.

(2
0
1
6
b
)

T
o
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xp
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re

w
h
y
n
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rs
e
s
ch
o
se

to

re
m
ai
n
in

th
e
W
e
st
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rn

A
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st
ra
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w
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rk
fo
rc
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to

d
e
ve
lo
p
in
si
g
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ts

in
to

th
e
ro
le

o
f

re
si
li
e
n
ce

o
f
n
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s
an
d
to

id
e
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fy

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e
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y
ch
ar
ac
te
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st
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s

o
f
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e
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ce

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is
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ye
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se

n
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R
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o
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-d
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s

T
h
e
m
at
ic

an
al
ys
is

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ig
h

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p
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et

al
.

(2
0
1
6
a)

T
o
e
xp
lo
re

re
si
d
e
n
ti
al

ag
e
d
ca
re

n
u
rs
e
s
w
o
rk
in
g
in

in
te
ri
m
,

re
h
ab
il
it
at
io
n
an
d
re
si
d
e
n
ti
al

ag
e
d
ca
re

p
e
rc
e
p
ti
o
n
s
o
f

re
si
li
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ce
.

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si
li
e
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ce

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e
m
al
e
s

P
o
rt
ra
it
u
re

an
d

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te
rp
re
ti
ve

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u
al
it
at
iv
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F
ie
ld

n
o
te
s,
m
e
m
o
s
an
d

g
e
st
u
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d
ra
w
in
g
s

in
te
rv
ie
w
s

T
h
e
m
at
ic

an
al
ys
is

H
ig
h

(C
on

ti
n
u
ed
)

© 2019 Australian College of Mental Health Nurses Inc.

10 E. BADU ET AL.

T
A
B
L
E

1
:
(C

o
n
ti
n
u
e
d
)

In
cl
u
d
e
d

ar
ti
cl
e

O
b
je
ct
iv
e
s

T
ar
g
e
t

G
e
n
d
e
r

S
tu
d
y
d
e
si
g
n

M
e
th
o
d
s

D
at
a
co
ll
e
ct
io
n
in
st
ru
m
e
n
t

A
n
al
ys
is

Q
u
al
it
y

sc
o
re

C
ra
ig
ie

et
al
.

(2
0
1
6
)

T
o
e
va
lu
at
e
th
e
fe
as
ib
il
it
y
o
f
a

m
in
d
fu
ln
e
ss
-b
as
e
d
in
te
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e
n
ti
o
n

ai
m
e
d
at

re
d
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ci
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g
co
m
p
as
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n

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ti
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an
d
im

p
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m
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n
al

w
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ll
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n
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s

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t

re
p
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e
d

Q
u
as
i-

e
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m
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n
ts

Q
u
an
ti
ta
ti
ve


P
at
ie
n
t
H
e
al
th

Q
u
e
st
io
n
n
ai
re
-9
;


S
h
o
rt

S
cr
e
e
n
in
g
S
ca
le

fo
r

D
S
M
-I
V
P
T
S
D
;


C
A
G
E

q
u
e
st
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n
n
ai
re
;


T
h
e
D
e
m
o
g
ra
p
h
ic

Q
u
e
st
io
n
n
ai
re
;


P
ro
fe
ss
io
n
al

Q
u
al
it
y
o
f

L
if
e
S
ca
le
;
D
e
p
re
ss
io
n

A
n
xi
e
ty

S
tr
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ss

S
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s;


S
p
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l
B
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r

S
ta
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ra
it

A
n
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e
ty

In
ve
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ry

fo
rm

Y
2
;


C
o
n
n
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r-
D
av
id
so
n

R
e
si
li
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n
ce

S
ca
le
;


P
as
si
o
n
fo
r
W
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rk

S
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le

D
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ve

an
d
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st
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cs

H
ig
h

C
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e
d
y
et

al
.

(2
0
1
7
)

T
o
in
ve
st
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at
e
th
e
p
re
va
le
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ce

o
f

b
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rn
o
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t,
d
e
p
re
ss
io
n
,
an
xi
e
ty

an
d
st
re
ss

in
A
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st
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li
an

m
id
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e
s

W
o
rk
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ce

st
re
ss

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m
al
e

C
ro
ss

se
ct
io
n
al

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u
an
ti
ta
ti
ve


C
o
p
e
n
h
ag
e
n

B
u
rn
o
u
t
In
ve
n
to
ry

(C
B
I)
;


D
e
p
re
ss
io
n
,
A
n
xi
e
ty

an
d

S
tr
e
ss

S
ca
le

(D
A
S
S
)

D
e
sc
ri
p
ti
ve

st
at
is
ti
cs

H
ig
h

D
o
la
n
et

al
.

(2
0
1
2
)

T
o
u
n
d
e
rt
ak
e
an

in
d
u
ct
iv
e

p
ro
ce
ss

to
b
e
tt
e
r
u
n
d
e
rs
ta
n
d

th
e
st
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ss
o
rs

an
d
th
e
co
p
in
g

st
ra
te
g
ie
s
u
se
d
b
y
re
n
al

n
u
rs
e
s

th
at

m
ay

le
ad

to
re
si
li
e
n
ce
.

W
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rk
p
la
ce

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ss

an
d

R
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si
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e
n
ce

F
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m
al
e
s

an
d

m
al
e
s

G
ro
u
n
d
e
d
th
e
o
ry

Q
u
al
it
at
iv
e


In
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Statistics homework help

Data.xlsx

Q1

NozzleDesign JetVelocity Shape
1 11.73 0.78
1 14.37 0.80
1 16.59 0.81
1 20.43 0.75
1 23.46 0.77
1 28.74 0.78
2 11.73 0.85
2 14.37 0.85
2 16.59 0.92
2 20.43 0.86
2 23.46 0.81
2 28.74 0.83
3 11.73 0.93
3 14.37 0.92
3 16.59 0.95
3 20.43 0.89
3 23.46 0.89
3 28.74 0.83
4 11.73 1.14
4 14.37 0.97
4 16.59 0.98
4 20.43 0.88
4 23.46 0.86
4 28.74 0.83
5 11.73 0.97
5 14.37 0.86
5 16.59 0.78
5 20.43 0.76
5 23.46 0.76
5 28.74 0.75

Q2

Time Job Operator
158.3 1 1
154.6 2 1
162.5 3 1
160 4 1
156.3 5 1
163.7 6 1
159.4 1 1
154.9 2 1
162.6 3 1
158.7 4 1
158.1 5 1
161 6 1
159.2 1 2
157.7 2 2
161 3 2
157.5 4 2
158.3 5 2
162.3 6 2
159.6 1 2
156.8 2 2
158.9 3 2
158.9 4 2
156.9 5 2
160.3 6 2
158.9 1 3
154.8 2 3
160.5 3 3
161.1 4 3
157.7 5 3
162.6 6 3
157.8 1 3
156.3 2 3
159.5 3 3
158.5 4 3
156.9 5 3
161.8 6 3

Q3

Pressure Temperature Yield Day
250 Low 86.3 1
250 Low 86.1 2
260 Low 84.0 1
260 Low 85.2 2
270 Low 85.8 1
270 Low 87.3 2
250 Medium 88.5 1
250 Medium 89.4 2
260 Medium 87.3 1
260 Medium 89.9 2
270 Medium 89.0 1
270 Medium 90.3 2
250 High 89.1 1
250 High 91.7 2
260 High 90.2 1
260 High 93.2 2
270 High 91.3 1
270 High 93.7 2

Q4

Vendor Heat Bar Size Strength
1 1 1 1.23
1 1 1 1.259
1 1 1.5 1.316
1 1 1.5 1.3
1 1 2 1.287
1 1 2 1.292
2 1 1 1.301
2 1 1 1.263
2 1 1.5 1.274
2 1 1.5 1.268
2 1 2 1.247
2 1 2 1.215
3 1 1 1.247
3 1 1 1.296
3 1 1.5 1.273
3 1 1.5 1.264
3 1 2 1.301
3 1 2 1.262
1 2 1 1.346
1 2 1 1.4
1 2 1.5 1.329
1 2 1.5 1.362
1 2 2 1.346
1 2 2 1.382
2 2 1 1.346
2 2 1 1.392
2 2 1.5 1.384
2 2 1.5 1.375
2 2 2 1.362
2 2 2 1.328
3 2 1 1.275
3 2 1 1.268
3 2 1.5 1.26
3 2 1.5 1.265
3 2 2 1.28
3 2 2 1.271
1 3 1 1.235
1 3 1 1.206
1 3 1.5 1.25
1 3 1.5 1.239
1 3 2 1.273
1 3 2 1.215
2 3 1 1.315
2 3 1 1.32
2 3 1.5 1.346
2 3 1.5 1.357
2 3 2 1.336
2 3 2 1.342
3 3 1 1.324
3 3 1 1.315
3 3 1.5 1.392
3 3 1.5 1.364
3 3 2 1.319
3 3 2 1.323

Q5

ToolAngle Viscosity FeetRate CuttingFluid SurfaceRoughness
12 300 10 no 0.00340
15 300 10 no 0.00362
12 400 10 no 0.00301
15 400 10 no 0.00182
12 300 15 no 0.00280
15 300 15 no 0.00290
12 400 15 no 0.00252
15 400 15 no 0.00160
12 300 10 yes 0.00336
15 300 10 yes 0.00344
12 400 10 yes 0.00308
15 400 10 yes 0.00184
12 300 15 yes 0.00269
15 300 15 yes 0.00284
12 400 15 yes 0.00253
15 400 15 yes 0.00163

Q6

Machine Power Station Yield
1 1 1 34.1
1 1 1 30.3
1 1 1 31.6
1 2 1 24.3
1 2 1 26.3
1 2 1 27.1
2 1 1 31.1
2 1 1 33.5
2 1 1 34
2 2 1 24.1
2 2 1 25
2 2 1 26.3
3 1 1 32.9
3 1 1 33
3 1 1 33.1
3 2 1 24.2
3 2 1 26.1
3 2 1 25.3
1 1 2 33.7
1 1 2 34.9
1 1 2 35
1 2 2 28.1
1 2 2 29.3
1 2 2 28.6
2 1 2 33.1
2 1 2 34.7
2 1 2 33.9
2 2 2 24.1
2 2 2 25.1
2 2 2 27.9
3 1 2 33.8
3 1 2 33.4
3 1 2 32.8
3 2 2 23.2
3 2 2 27.4
3 2 2 28
1 1 3 36.2
1 1 3 36.8
1 1 3 37.1
1 2 3 25.7
1 2 3 26.1
1 2 3 24.9
2 1 3 32.8
2 1 3 35.1
2 1 3 34.3
2 2 3 26
2 2 3 27.1
2 2 3 23.9
3 1 3 33.6
3 1 3 32.8
3 1 3 31.7
3 2 3 24.7
3 2 3 22
3 2 3 24.8

assignment.pdf

Final Exam: STAT4504
Statistical Design and Analysis of Experiments

Due: 4:00 pm Thursday, April 28, 2022

The deadline for the final exam is set as per Carleton University’s take home exam policy.

Instructions for submission: Convert your document to a PDF file. Upload the generated pdf via
Gradescope under Final Exam. All programming needs to be completed with SAS or R as stated in the course
outline. The assignment needs to be uploaded in Gradescope. Make sure when you upload, you specify which
page corresponds to which question.
The datasets for the final exam are available in an excel file “Data_Final.xlsx”. The dataset for each question
is given in a different sheet so make sure you use the appropriate sheet for appropriate analysis.

For each question on data analysis, you must

a. Select an appropriate statistical model to analyze the dataset based on the information provided in
the question and provide justification for your choice of model.

b. Provide the appropriate ANOVA table with two additional columns that shows
i. The expected values of the appropriate mean square terms under the model of your choice.

ii. The expected values of your test statistics as the ratio of the appropriate mean square terms
based on your model.

c. Clearly state the null and alternate hypothesis, distribution of the test statistics under the null
hypothesis, appropriate F-value or p-value that you are using to make the decision and your
conclusion. Note: your null hypothesis is different for fixed effects and random effects.

d. Perform appropriate residual analysis and comment on the model adequacy.
e. If model assumptions are not valid, suggest an appropriate transformation and provide justification

for the transformation. Refit the model with the appropriate transformation and state your
conclusion including comments on the model adequacy. Make sure to state the appropriate null and
alternate hypotheses.

Note: If you choose to use Box-Cox transformation in SAS using the proc transreg function, use the class()
to specify dependent categorical variables and for continuous variables, use the identity() to specify the
dependent continuous variables.

1. (15 points) An article in the Fire Safety Journal (“The Effect of Nozzle Design on the Stability and

Performance of Turbulent Water Jets,” Vol. 4, August 1981) describes an experiment in which a shape factor
was determined for several different nozzle designs at six levels of jet efflux velocity. Interest focused on
potential differences between nozzle designs, with velocity considered as a nuisance variable. The data are
shown below:

Does the nozzle design influence the shape or the transformed shape (if transformation was needed)?

Chidera Eleh
Chidera Eleh

2. (20 points) To simplify production scheduling, an industrial engineer is studying the possibility of assigning
one time standard to a particular class of jobs, believing that differences between jobs is negligible. To see
if this simplification is possible, six jobs are randomly selected. Each job is given to the same three randomly
selected operators. Each operator completes the job twice at different times during the week, and the
following results are obtained. Use an appropriate model to test whether the engineer’s belief is justifiable.

3. (20 points) The yield of a chemical process is being studied. The two factors of interest are temperature and
pressure. Three levels of each factor are selected; however, only nine runs can be made in one day. The
experimenter runs a complete replicate of the design on each day. The data are shown in the following table:

Identify which factors affect the yield or the transformed yield (if transformation was needed).

4. (20 points) A structural engineer is studying the strength of aluminum alloy purchased from three vendors.
Each vendor submits the alloy in standard-sized bars of 1.0, 1.5, or 2.0 inches. The processing of different
sizes of bar stock from a common ingot involves different forging techniques, and so this factor may be
important. Furthermore, the bar stock is forged from ingots made in different heat and thus, three different
heat categories were selected randomly. Each vendor submits two tests specimens for each treatment
combination categories. The resulting strength data is shown in the table below. Analyze the data and
what combination of various treatments would you recommend if the engineer is interested in having
aluminum alloy with highest strength.

5. (30 points) An engineer has performed an experiment to study the effect of four factors on the surface

roughness of a machined part. The factors (and their levels) are A = tool angle (12 degrees, 15 degrees), B

= cutting fluid viscosity (300, 400), C = feed rate (10 in/min, 15 in/min), and D = cutting fluid cooler used
(no, yes). The data from this experiment (with the factors coded to the usual -1, +1 levels) are shown
below.

a) Using the data provided, create a one-half fractional design such that the resulting design is of the

highest resolution. Estimate the model effects and select a tentative model and check for model
adequacy. Perform any transformation if needed.

b) Drop any factor that does not seem to be important and analyze the data as a full factorial model
with only significant factors from (a). Compare your results with those obtained in part (a).
Note: For this question, only provide the additional two columns in the ANOVA table for the final
model selected in (b). Provide a fitted regression model when the factors are coded variables.

6. (20 points) A process engineer is testing the yield of a product manufactured on three machines. Each

machine can be operated at two power settings. Furthermore, a machine has three stations on which the
product is formed. An experiment is conducted in which each machine is tested at both power settings, and
three observations on yield are taken from each station. The runs are made in random order, and the results
are shown in Table below.

Identify which factors affect the yield or the transformed yield (if transformation was needed).

7. (15 points) In a completely randomized design (i.e., with one factor), show that
𝐸(𝑀𝑆!) = 𝜎”

Statistics homework help

Statistical Analysis

1. Analysis of Variance

2. Chi-Square and Other Non-Parametric Tests

3. Sample Size and Statistical Power

1. You wish to conduct an ANOVA (one way/omnibus) in your capstone project. In order to insure you have enough power to detect differences in your sample, you need to run a power analysis in G*Power. Assume that you are expecting a medium effect size, α = 0.05, and a minimum power of 0.80. Your experiment utilizes three (3) groups. What is the required sample size (a priori)? How many data points should exist in each group?

2. You conducted a Chi-Square Goodness of Fit Test in your capstone project. Unfortunately, you did not get the sample size you had hoped for during your research. You were able to get 55 in the sample. Calculate your actual power (post hoc). You did a 2 X 2 table. Assume you had a medium effect size.

3. You conducted a t-test in your capstone research. You found a statistically significant difference between your groups even though your sample size was relatively small. Upon conducting a post hoc power analysis you found that your actual power was 0.65. What should you do? Is there a problem with having a power less than 0.80 when you have significant differences?

4. You conducted a t-test in your capstone research. You did not find a statically significant difference between your groups even though your sample size was relatively small. Upon conducting a post hoc power analysis you found that your actual power was 0.57. What should you do? Is there a problem with having power less than 0.80 when you do not have significant differences?

Statistics homework help

Homework I

From Matt Teachout’s Statistics Website

Collecting and Analyzing Data:

From Matt Teachout’s Online Book (See Canvas Statistics Part I)

-Problem Set Section 1A: question 2

-Problem Set Section 1B: questions 2, 4, 6, 8, 10, 12, 14

-Problem Set Section 1C: questions 2, 4, 6, 8, 10

-Problem Set Section 1D: questions 18, 20

-Problem Set Section 1E: questions 18, 22, 26

-Problem Set Section 1F: questions 4, 8, 16, 22

-Problem Set Section 1G: questions 4, 8, 14

Probability:

From Combinatorics and Probability Notes (See Canvas Statistics Part I)

-Section 13.1: questions 22, 24 (page 9)

-Section 13.2: question 12 (page 14)

-Section 13.3: questions 14, 30 (page 21)

-Section 13.4: questions 16, 20 (page 29)

-Section 13.5: questions 4, 12 (page 36)

-Section 13.6: question 14 (page 43)

Statistics homework help

STAT 134 Mini Project Rubric

1 Introduction

In this semester, one mini-project of writing a 2-3 page report will be assigned.
The objective of this mini-project is to deepen your understanding of the class
material, and to give you a sense of how the class materials can be applied to
real-world problems. 6 topics will be given below as a guideline, but you can also
choose your own topic as long as the topic is relevant to the course materials.
Students must work in pairs and submit a single joint report. We suggest you
reach out to your classmates from section, class, at the SLC, or on Piazza to
find a partner.

2 Timeline

April 1 2022, 10pm – ONLY IF your topic is not from the given 6
topics: Your topic must be approved via Private Piazza post. Please
don’t leave this to the last minute.

May 1 2022, 10pm : Due Date (one of the partners uploads on Grade-
scope —we don’t want duplicate submissions)

3 Detailed Instructions

• Your report should contain the following 4 elements:

1. The title and names of two authors. A footnote indicating how each
student contributed.

2. How the topic is related to the class material.

3. Proof (if applicable) and theoretical background of the topic

4. Two examples of how the topic can be applied in a real-world prob-
lem. One of the examples may be the example topic itself.

• If you choose your own topic, make sure to send a private Piazza post to
get our OK about the project.

• The report should be typed 2-3 pages plus references, and be no longer
than 3 pages.

1

4 Grading

You will receive a score out of 4 based on the criteria below.

4 : The report is exceptional. (Only few students will get it)

3 : The report contains all the 4 elements written above.

2 : The report only provides the proof and theoretical background OR
examples of how the topic is applied.

1 : The report does not contain enough information.

0 : Report is not submitted

5 Example Topics (Related concept)

1. Nash Equilibrium in Game theory (Expectation) 1

2. Simple linear regression (Bivariate normal, correlation) 2

3. A/B testing, Fisher exact test (Normal distribution / Counting) 3

4. The German Tank Problem (Bias Variance Trade-off) 4

5. Confidence Interval Interpretation (Parameter estimation)5

6. Harvard Medical School Survey (Bayes’ Rule)6

7. Others – some other application of a concept taught in the class.

1see https://en.wikipedia.org/wiki/Nash_equilibrium
2see http://stat88.org/textbook/notebooks/intro section 12.1
3see http://stat88.org/textbook/notebooks/intro section 9.2
4see http://stat88.org/textbook/notebooks/intro section 11.2
5see http://stat88.org/textbook/notebooks/intro sections 9.2,9.3
6see http://stat88.org/textbook/notebooks/intro section 2.4

2

  • Introduction
  • Timeline
  • Detailed Instructions
  • Grading
  • Example Topics (Related concept)

Statistics homework help

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Statistics homework help

Final Project: Digital Marketing Analytics Project

The final digital marketing analytics project focuses on answering specific questions about the current digital marketing campaign of a business. You will first analyze the digital marketing presence (website, advertisement, or social media presence) of a business. Based on your analysis, your group will develop research questions, collect and analyze the data, and draw insightful conclusions based on statistical analyses.

Project Deliverables and Deadline

Grade

Due

Proposal

40 points (4% of the final grade)

Mar 3

Project Presentation

40 points (4% of the final grade)

Apr 26, 28 in class

Project Report

150 points (15% of the final grade)

May 5 11:59 PM

Business client selection

· Businesses can range from one-man local shops to multi-national companies.

· If you plan to collect the data from the survey, choose a business that is relevant to your survey sample. You will distribute the A/B testing survey to students taking this class.

· Choose a business that has enough activity for you to analyze. Select a business that has at least 4 landing pages (i.e., webpages) on its website and it is a plus if the client has sufficient social media activities.


Important: Data Requirement

· Your project outcome should be based on the
original data
. You can collect your data from the existing database (e.g., YouTube, Instagram, Twitter, Google Trends, etc.) or from the Qualtrics survey (e.g., A/B testing survey).

· To ensure reliable and valid results, the number of observations (i.e., the number of survey respondents of A/B testing survey; the number of videos, social media posts, Tweets, influencers in other projects) should be at least 140.

· For meaningful data exploration, your data should contain a minimum of 15 variables (the number of questions of your survey; the number of variables in other projects).

NOTE: If you would like to study different questions for the final project, please consult with me in advance. I am open to your suggestions if (1) the topic is relevant to digital marketing, (2) the analysis builds on the original data, and (3) your hypotheses are tested with statistical analyses (e.g., regression analysis). Examples of the topics you may consider include:

“What makes YouTube videos viral?”

“What drives engagement in Instagram posts?”

“What makes Kickstarter projects more successful?”

“The impacts of the Covid-19 Pandemic on Kickstarter project successes”

1. Project Proposal

Student groups are expected to submit the project proposal by 11:59 PM on Mar 3. The proposal provides you with opportunities to prepare the project step-by-step and improve your research questions and data collection plan based on my feedback. The project proposal is worth 4% of the final grade.


Report Format

– PDF or Word document

12-point Times font, 1-inch page margins, US Letter paper, left-justification, 1.5 line spacing

Maximum 3 pages except for the draft of the survey questionnaire and data codebook.

Your report will be evaluated based on the following components (Total 40 points).

1. Understanding of client’s situation and research motivation (10 points)

2. Quality of research questions and hypotheses (10 points)

3. Quality of data collection plan (20 points)

You should provide the following information in your proposal.

· Client Profile

· Research motivation

· Research questions

· Research hypotheses

· Research design and data collection plan

· Required appendix: Qualtrics survey link and codebook (A/B testing survey) or codebook (other projects)

Client Profile:

· Name, Location, URL, social media channels

· Goods and services offered

· Overview of their digital presence (e.g., website, social media posts, search ads, display ads, email marketing, etc.)

Research Motivation and Research Questions:

· Do you see any problems or areas for improvement? How can your research project help improve your client’s digital marketing?

· Specify your research objectives and research questions.

· Research questions should be meaningful and relevant for your client that potentially presents actionable insights to improve the client’s digital marketing presence.

Research Hypotheses

· Craft at least 5 research hypotheses

you plan to test.

· Research hypotheses should be clearly stated and be tested with statistical analyses.

· State
at least 2 hypotheses
on the interaction effects.

[AB Testing: Example of research hypotheses]

· Focusing on the differences between version A and B (main effect)

· Version A drives more likes on Instagram than Version B.

· Customers find Version A more energetic than Version B.

· Focusing on the differences across customer segments (interaction effect)

· The degree of liking Version A over Version B depends on gender. The degree of liking Version A (compared to Version B) is weakened for females (strengthened for males).

· The degree of liking Version A over Version B depends on customers’ fashion trendiness. The degree of liking Version A (compared to Version B) is weakened for fashion trendy customers (strengthened for less fashion trendy customers.)

[Other projects: Example of research hypotheses]

· Focusing on the main effects

· The number of hashtags is positively related to the number of likes on Instagram.

· The number of people featured in the post is positively related to the number of likes on Instagram.

· Posts posted in the evening receive more likes than posts posted in the afternoon.

· Focusing on the interaction effects

· The positive relationship between the number of hashtags and the number of likes is strengthened for fashion Instagrammers.

Research Design/ Data Collection Plan

[AB Testing survey]

· Present an example of your version A and B: provide an image

· Timeline of survey and survey distribution plan

· Sample of your survey

· What to measure?

· List at least 3 dependent variables: How would you compare the performance of two versions?

· List customer characteristics that are potentially relevant to your A/B test.

[Other projects]

· If you plan to collect the data from the existing database (e.g., YouTube, Instagram, Twitter, Google Trends, government data, etc.)

· Source of the data

· Sampling plan:

· Specify the sampling criteria to select 140 YouTube videos, social media posts, etc.

· Timeline of the data collection plan

· What to measure?

· Define dependent variables: What is your focus of the research? (e.g., number of likes, number of shares, number of views, viewing duration, etc.)

· List other variables that are potentially relevant to your dependent variable.

Required appendix for any projects

· Link to your Qualtrics survey

· Data codebook

· Present how each variable is measured.

· Column1: variable name

· Column2: variable description

· Column3: Is it your dependent variable?

· Column4: Is it measured on a nominal scale? (i.e., categorical variable)

2. Project Presentation


Deliverable:
PowerPoint slides that summarize the key findings of your final project (slides submission due 11:59 PM on the day before your presentation day) Each group will be given 18 -20 minutes.

Please make sure to deliver the following elements in your presentation:

· Client overview and research motivation

· Research questions and hypotheses

· Research design and data description

· Summary of findings

· Conclusions, recommendations, suggestions

Your report will be evaluated based on the following components (Total 40 points).

1. Organization of presentation, effective use of tables and figures (15 points)

2. Understanding of research project findings (including the quality of Q&A) (15 points)

3. Presentation and communication skills (clarity and enthusiasm) (10 points)


3. Project Report


Report Format

– PDF or Word document

12-point Times font, 1-inch page margins, US Letter paper, left-justification, 1.5 line spacing

Maximum 12 pages except for references and appendices.

Your report will be evaluated based on the following components (Total 150 points).

1. Executive Summary (10 points)

2. Business Overview (20 points)

3. Research Design (30 points)

4. Findings from Statistical Analyses (50 points)

5. Conclusion and Recommendations (20 points)

6. Communication and Readability (20 points)

1. Executive Summary (5 points, maximum one page)

This stand-alone document provides your client with a project snapshot and highlights four key areas:

· Purpose – a basic review of the project by introducing research objectives.

· Methods – an overview of research design and data

· Key Results – major findings of the project.

· Conclusion – a clear synthesis of the report content. This is your chance to tie together the findings and focus on recommendations for your client.

2. Client Overview and Research Motivations (10 points, 1-2 pages)

This section should provide an overview of the client and research objectives.

Client Profile:

· Name, Location, URL

· Goods and services offered

Market Analysis:

· Current and potential customers

· Current and potential competitors

· Market position and unique selling points of the goods/services offered

Current Marketing:

· Strengths and weaknesses of digital marketing presence

· Social media, website design, search ad, display ad, etc.

· If available, summary information from other third-party web tracking service (e.g., Similar Web, SEMRush, etc.)

Objectives of your research:

· Clearly state your research objectives and questions

· Justify how your research can help the business

3. Research Design (25 points, 2-3 pages)

This section should provide an overview of research design. This section should include:

· Research hypotheses:

· List at least 6 hypotheses

· Explore potential differences across respondents/observations in your data

· Research Design and Data Description

· Data collection process: timeline, sample, A/B test design

· Data Description

· Description of your data

· [Required table] Codebook: describe how each variable is coded in your data

· [Required appendix] Qualtrics survey questions and links (if you collected the data from Qualtrics survey)

4. Findings (50 points, 4-6 pages including tables and figures)

· Descriptive analysis

· Summary of survey respondents/ observations

· Summary of key variables

· Include appropriate graphical and numerical summaries (i.e., bar graphs, pie charts, boxplots, scatterplots, counts, correlation coefficients)

· (For A/B testing) Exploratory Difference analysis of the key dependent variables. Focus on meaningful differences.

· Discuss whether you were able to see the differences in your key dependent variables between version A and B.

· Regression analysis that provides an answer to research questions.

· Propose at least four different regression models and summarize the results.

· Must present a model that tests the differences across observations using the interaction effects.

· Select the best model and discuss the findings based on the best regression model.

· Discuss what the data tell you about your research questions. What did you learn?

5. Conclusion (15 points, 1-2 pages)

· Summary of your answers to research questions

· Recommendations and implications for client that describes implications of findings for marketing managers and relevant stakeholders

· Limitations & Suggestions for future research.

4. Communication and readability (15 points)

Your presentation should have a logical flow, be easy to follow, and clear. Feel free to utilize charts, tables, and figures to illustrate your content.


Required Appendix

· Survey questionnaire

· Data and codebook

· Descriptive summary statistics of all your variables

· Additional regression analysis tables


References

· Make sure to include links/screenshots or whatever is necessary to demonstrate your points.

· Please provide the list of references in the slides’ notes (sources of articles, industry reports, blog posts, web links, etc.)

· Always provide with an appropriate reference for your argument.

· The best reports will be factual and analytical. There is no room for personal feelings or emotional response. Think of this as the type of presentation created by a digital marketing consulting firm before a first meeting with a client.

1

Statistics homework help

MGT 3410 Homework 5 Spring 2022

EOQ

1. Ross White’s machine shop uses 2500 brackets during the course of a year, and this usage is relatively constant throughout the year. These brackets are purchased from a supplier 100 miles away for $15 each, and the lead time is 2 days. The holding cost per bracket per year is $1.50 (or 10% of the unit cost) and the ordering cost per order is $18.75. There are 300 working days per year.

a. Develop a total cost model for this system.

b. What is the EOQ for this problem?

c. What is the cycle time?

d. What is the reorder policy?

e. What are the total annual holding and ordering costs associated with your recommended EOQ?

f. What is the total annual cost associated with your recommended EOQ?


Due Date: Apr 21, 11:59pm

Note: Homework solution must be submitted electronically to Homework 5 folder in “Assignments” on D2L.

It is your choice to submit all of your work or just the final answer only. If you only submit the final answer and the answer is wrong, you will lose all the points assigned to that question. If you also show the steps how you get that answer, you still can earn partial credit as long as the steps are not completely wrong.

Statistics homework help

NH1516

Respondent sequence number Gender Age in years at screening Race/Hispanic origin Education level – Adults 20+ Marital status Annual family income Ratio of family income to poverty Weight (kg) Standing Height (cm) Body Mass Index (kg/m**2) Waist Circumference (cm) 60 sec. pulse (30 sec. pulse * 2) Systolic: Blood pres (3rd rdg) mm Hg Diastolic: Blood pres (3rd rdg) mm Hg White blood cell count (1000 cells/uL) Lymphocyte percent (%) Monocyte percent (%) Segmented neutrophils percent (%) Eosinophils percent (%) Basophils percent (%) Lymphocyte number (1000 cells/uL) Monocyte number (1000 cells/uL) Segmented neutrophils num (1000 cell/uL) Eosinophils number (1000 cells/uL) Basophils number (1000 cells/uL) Red blood cell count (million cells/uL) Hemoglobin (g/dL) Hematocrit (%) Mean cell volume (fL) Mean cell hemoglobin (pg) MCHC (g/dL) Red cell distribution width (%) Platelet count (1000 cells/uL) Mean platelet volume (fL) Ever used marijuana or hashish Age when first tried marijuana Used marijuana every month for a year? Age started regularly using marijuana How often would you use marijuana? How many joints or pipes smoke in a day? # days used marijuana or hashish/month Ever used cocaine/heroin/methamphetamine Age first used cocaine Ever used heroin Age first used heroin Ever used methamphetamine Age first used methamphetamine Fasting Glucose (mg/dL) Fasting Glucose (mmol/L) Direct HDL-Cholesterol (mg/dL) Direct HDL-Cholesterol (mmol/L) Insulin (uU/mL) Insulin (pmol/L) Insulin Comment Code Total length of ‘food fast’, hours Total length of ‘food fast’, minutes
83732 1 62 3 5 1 10 4.39 94.8 184.5 27.8 101.1 76 116 62 9.8 23.9 8.2 63.5 4 0.5 2.3 0.8 6.2 0.4 0 4.93 15.2 44.7 90.8 30.8 34 13.9 181 8.3 1 2 1 46 1.19
83733 1 53 3 3 3 4 1.32 90.4 171.4 30.8 107.9 72 134 82 7.3 31.3 9.7 54.8 2.6 1.8 2.3 0.7 4 0.2 0.1 4.89 17.5 49.7 101.8 35.8 35.1 13.4 170 9.6 2 2 101 5.59 63 1.63 17.26 103.56 0 12 2
83734 1 78 3 3 1 5 1.51 83.4 170.1 28.8 116.5 56 136 46 4.4 29.9 9.6 55.8 3.9 0.9 1.3 0.4 2.5 0.2 0 4.18 12.4 37.9 90.8 29.6 32.6 14.7 223 9 84 4.66 30 0.78 11.77 70.62 0 10 27
83735 2 56 3 5 6 10 5 109.8 160.9 42.4 110.1 78 136 70 6.1 17.1 10.3 68.7 3.1 0.9 1 0.6 4.2 0.2 0.1 4.54 12.8 40.1 88.3 28.2 31.9 13.1 280 9.1 2 2 61 1.58
83736 2 42 4 4 3 7 1.23 55.2 164.9 20.3 80.4 76 98 56 4.2 47.1 7.8 44.8 0.2 0.2 2 0.3 1.9 0 0 4.16 12.1 36.5 87.8 29.1 33.2 12.3 275 7.7 1 25 1 25 5 4 30 2 84 4.66 53 1.37 5.42 32.52 0 10 35
83737 2 72 1 2 4 14 2.82 64.4 150 28.6 92.9 64 120 60 6.1 31.7 8.5 56.6 2.8 0.5 1.9 0.5 3.5 0.2 0 4.38 13.4 40.6 92.6 30.5 33 14.1 123 10.1 107 5.93 78 2.02 8.24 49.44 0 12 25
83738 2 11 1 6 1.18 37.2 143.5 18.1 67.5 78 100 56 9 36.8 4.3 56.9 1.7 0.4 3.3 0.4 5.1 0.2 0 4.65 13.7 40 86.2 29.4 34.1 13.2 280 7 43 1.11
83739 1 4 3 15 4.22 16.4 102.1 15.7 48.5 7.8 47.4 7.6 41.9 2.9 0.3 3.7 0.6 3.3 0.2 0 4.15 11.5 33.4 80.5 27.6 34.4 14 223 7.8
83740 1 1 2 77 10.1
83741 1 22 4 4 5 7 2.08 76.6 165.4 28 86.6 66 112 74 3.5 38.2 10.6 39.7 10.3 1.3 1.3 0.4 1.4 0.4 0 5.63 15.4 46.8 83.2 27.3 32.8 13.1 210 7.7 1 15 1 16 4 2 25 2 95 5.27 48 1.24 11.39 68.34 0 9 51
83742 2 32 1 4 1 6 1.03 64.5 151.3 28.2 93.3 74 120 72 8.3 35.4 6.7 56 1.3 0.8 2.9 0.6 4.6 0.1 0.1 4.45 13.1 38.6 86.7 29.4 33.9 12.9 236 7.6 1 18 2 2 28 0.72
83743 1 18 5 15 5 72.4 166.1 26.2 5.8 26.3 10.4 58.7 4.2 0.6 1.5 0.6 3.4 0.2 0 5.4 16 48.3 89.5 29.7 33.2 12.5 269 7 2 2 97 5.38 53 1.37 11.4 68.4 0 10 10
83744 1 56 4 3 3 3 1.19 108.3 179.4 33.6 116 70 180 104 6.1 31.7 8.3 57.6 1.7 0.8 1.9 0.5 3.5 0.1 0 4.6 13.9 42.1 91.5 30.2 33 12.3 146 10.3 1 18 2 1 20 2 2 52 1.34
83745 2 15 3 4 0.86 71.7 169.2 25 88.3 92 106 76 8.5 24.3 6.9 65.2 3.1 0.5 2.1 0.6 5.5 0.3 0 4.38 13.8 40.4 92.2 31.5 34.2 12.4 286 7.2 43 1.11
83746 2 4 5 12 17.7 105 16.1 56.5
83747 1 46 3 5 6 3 0.75 86.2 176.7 27.6 104.3 68 150 92 8.3 23.4 6.4 67 2.2 1 1.9 0.5 5.6 0.2 0.1 5.25 15.2 46.8 89.3 29 32.4 14.2 268 8.2 2 2 44 1.14
83748 1 3 4 6 0.94 17.3 103.6 16.1 52.5
83749 2 17 3 14 3.16 75.9 161.7 29 98.3 80 112 62 9 28.5 7.5 63.3 0.5 0.3 2.6 0.7 5.7 0 0 4.45 12.7 38.7 86.9 28.7 33 12.8 292 8 88 4.88 42 1.09 16 96 0 14 34
83750 1 45 5 2 5 4 1.36 76.2 177.8 24.1 90.1 64 108 74 5.1 42.8 14.2 39.5 2.7 0.9 2.2 0.7 2 0.1 0 5.03 15.4 46.9 93.1 30.5 32.7 13.2 156 9.2 1 21 2 1 1 21 2 1 21 84 4.68 50 1.29 2.86 17.16 0 11 0
83751 2 16 1 4 0.58 51.7 152.6 22.2 74.2 80 106 54 9.1 22.6 12.7 62.1 2.1 0.7 2.1 1.2 5.7 0.2 0.1 4.53 12.4 37.1 82.1 27.4 33.3 15.7 279 9.3 55 1.42
83752 2 30 2 4 6 15 5 71.2 163.6 26.6 90.7 60 104 50 9.8 19.7 6.7 72.4 0.7 0.6 1.9 0.7 7.1 0.1 0.1 4.46 14.3 40.8 91.5 31.9 34.9 13.1 269 7.7 1 14 2 2 67 1.73
83753 1 15 4 8 2.49 71.2 170.5 24.5 76.9 54 124 64 3.8 33.1 10.6 51.5 3.9 1.1 1.3 0.4 2 0.1 0 4.81 14.7 43.6 90.7 30.5 33.6 13.6 224 8.1 103 5.71 48 1.24 5.43 32.58 0 10 29
83754 2 67 2 5 1 6 0.89 117.8 164.1 43.7 123 66 116 76 5.9 37.5 10.6 46.8 4.1 1.2 2.2 0.6 2.8 0.2 0.1 5.22 15.7 45.9 87.8 30.1 34.3 13.2 209 8.2 2 130 7.24 50 1.29 32.89 197.34 0 14 34
83755 1 67 4 5 2 5 2.04 97.4 183.8 28.8 106.3 64 132 78 6.4 32.6 9 56.4 1.6 0.5 2.1 0.6 3.6 0.1 0 4.67 14.8 43.8 93.8 31.6 33.7 12.3 170 9 2 284 15.8 57 1.47 19.05 114.3 0 13 49
83756 1 16 3 7 1.11 60 163.9 22.3 76 68 120 70
83757 2 57 2 1 4 5 0.77 80.5 150.8 35.4 113.5 76 148 58 6.7 26.9 8.4 61.7 2.4 0.8 1.8 0.6 4.1 0.2 0.1 4.65 13.6 40.3 86.6 29.1 33.6 13.4 256 7.6 2 2 398 22.1 43 1.11 5.57 33.42 0 9 45
83758 1 80 3 5 2 9 4.71
83759 2 19 1 7 1.74 100.8 175.4 32.8 104.6 78 108 72 12.8 23.4 6.9 68.5 0.8 0.6 3 0.9 8.8 0.1 0.1 4.72 12.4 38.5 81.7 26.3 32.2 14 382 8.1 2 2
83760 2 3 4 7 1.1 14.6 94.7 16.3 47.5 7.2 53.4 8.4 32.1 5.7 0.6 3.8 0.6 2.3 0.4 0 4.7 12.6 37.9 80.6 26.7 33.2 13 503 6.8
83761 2 24 5 5 5 1 0 61.8 156.4 25.3 79.5 68 104 62 7.7 35.3 7.3 56.3 1 0.3 2.7 0.6 4.3 0.1 0 4.19 12.4 36.9 88.1 29.7 33.7 13.1 230 8.8 2 2 95 5.27 41 1.06 13.23 79.38 0 10 36
83762 2 27 4 4 5 6 2.12 107.9 168.5 38 114.8 76 138 70 8.3 25 3.1 71 0.6 0.4 2.1 0.3 5.9 0 0 4.34 10.8 34.1 78.5 24.9 31.8 12.7 259 8.7 34 0.88
83763 2 2 2 9 1.94 12.1 89.8 15 45.6
83764 1 14 3 15 5 54.8 170.8 18.8 69.8 78 102 60 4.5 41 6.1 49.7 2.3 1 1.8 0.3 2.2 0.1 0 4.85 14.6 41.6 85.8 30 35 12.6 284 8.4 369 20.5 39 1.01 30.1 180.6 0 11 36
83765 2 0 3 9 3.17 5.2
83766 2 10 3 14 3.34 51 160 19.9 76.6 90 112 54
83767 2 54 5 4 3 14 2.99 59 149.9 26.3 88.9 76 128 74 7.9 25.1 6 64 4.2 0.8 2 0.5 5.1 0.3 0.1 4.58 13.9 42.1 91.8 30.2 32.9 13.7 225 8.9 2 2 71 1.84
83768 2 15 3 6 1.09 52.4 158 21 73.6 72 108 62 9.7 26.2 7.8 64.8 1 0.3 2.5 0.8 6.3 0.1 0 4.48 13.9 40.3 90 31.1 34.6 12.8 206 9.7 51 1.32
83769 1 49 5 2 1 10 2.97 72.8 170.7 25 96.6 62 112 68 6.9 42 8.9 40.3 7.8 1.1 2.9 0.6 2.8 0.5 0.1 4.65 14 40.7 87.5 30.2 34.5 12.5 263 7 2 2 29 0.75
83770 1 15 4 4 0.66 48 162 18.3 63.6 60 110 42 5.2 25.8 10.8 60.5 2.3 0.7 1.3 0.6 3.1 0.1 0 5.06 14.6 42.6 84.3 28.9 34.2 13.2 216 8.6 99 5.5 68 1.76 4.33 25.98 0 13 59
83771 2 2 1
83772 2 2 5 5 1.25 15.2 93.8 17.3 50.6 17 28.8 7.3 54 9.6 0.4 4.9 1.2 9.2 1.6 0.1 4.56 12.3 36.3 79.8 27.1 33.9 13.1 471 6.8
83773 2 80 3 3 2 7 3.57 67.7 149.8 30.2 108.4 66 142 68 8.6 54.8 7.4 34.2 3.1 0.6 4.7 0.6 2.9 0.3 0.1 4.46 13.3 40.1 89.9 29.8 33.1 13.8 301 7.4 97 5.38 51 1.32 7.82 46.92 0 10 36
83774 2 13 3 15 4.3 55.9 169.7 19.4 76.8 80 106 72 5.8 38.1 6.9 52 2.5 0.6 2.2 0.4 3 0.1 0 4.38 12.7 37.5 85.7 29.1 33.9 13 261 8.1 51 1.32
83775 2 69 2 1 4 2 0.55 77.7 160.2 30.3 106.8 64 130 60 5.3 34.6 6.4 56.5 2.2 0.5 1.8 0.3 3 0.1 0 4.54 13.5 40.4 88.8 29.8 33.5 13.5 158 8.6 2 38 0.98
83776 2 58 1 5 1 14 3.72 56.6 157.5 22.8 83 70 112 60 6.8 30.7 7.6 57.9 3.2 0.8 2.1 0.5 3.9 0.2 0.1 4.18 13.1 39.2 93.8 31.2 33.4 13.2 241 8 72

Statistics homework help

INFERENTIAL STATISTICS FOR DECISION MAKING

Chapter-10

Effect Size, Confidence Intervals, and NHST: Two-Sample Designs

Use the following data set to answer the following questions. To earn full credit show all of your calculations and other work. Explain your answers. Don’t just write a number.

The 26 students who signed up for General Psychology reported their GPA. Each person was matched with another person on the basis of the GPAs, and two groups were formed. One group was taught with the traditional lecture method by Professor Nouveau. The other class could access the Web for the same lectures whenever they wished. At the end of the term, both classes took the same comprehensive final exam, and they also filled out a “Satisfaction Questionnaire.” Scores on both measures are shown below.

Analyze the data with t tests and effect size indexes. Write a conclusion.

You have to use the JASP Software (https://jasp-stats.org/download/) to perform your analysis. Make sure you include the analysis output in your submission. Also, explain your results in detail.

Comprehensive Final Exam Scores

Satisfaction

Scores

Traditional Section

Online Section

Traditional Section

Online Section

50

56

25

31

72

75

18

19

64

62

40

38

82

90

31

35

89

91

17

24

65

65

22

20

74

72

14

18

85

87

36

35

80

76

27

31

65

79

22

27

82

77

23

27

75

78

28

28

64

70

20

23

Statistics homework help

Lecture 4 Example Modified

Use this example for your HW assignment. This example differs from the lecture example.
Problem Statement
A 10″ well connect has been proposed to move 30,000 Mscfd of gas to a trunk line along with a six unit equity compressor station. It is assumed that the new well connect will take approximately one year to build and revenue will not be realized until year one. The flow rate will decline by 90% during the first year of well life and 5% for the remainder of the contract. The contract term is for 10 years only. Assume Labor cost will be 40% of year one revenue for time zero and time one and 30% of the revenue of each of the following years there after. Determine the cost of service at 13% company hurdle rate? What is the NPV of this project at the company hurdle rate? What is the actual rate of return for this project assuming a cost of service to be $0.5/MMBTU?
Initial values
Initial Flow Rate = 30000 Mscfd
Pipe Diameter = 10 in Nominal Pipe
Pipe Length = 5.25 miles
Gas Heating Value = 1100 BTU/scf
Costs and Price
Cost of Service = $0.0500 /MMBTU
Pipe Cost = $100,000.00 /in-mile
Six Unit Equity Compressor station = $13,000,000 /station
Company Hurdle Rate = 13.00%
Assume Labor cost is 30% of Revenue
Volumes
Volumes (Mscf) 0 10,950,000.00 1,095,000.00 547,500.00 273,750.00 136,875.00 68,437.50 34,218.75 17,109.38 8,554.69 4,277.34
Energy Volumes (MMBTU) 0 12,045,000.00 1,204,500.00 602,250.00 301,125.00 150,562.50 75,281.25 37,640.63 18,820.31 9,410.16 4,705.08
Cost Analysis
Year 0 1 2 3 4 5 6 7 8 9 10
Pipeline Costs = -$5,250,000.00
Compression Costs = -$13,000,000
Labor Costs = -$87,928,500.00 -$87,928,500.00 -$6,594,637.50 -$3,297,318.75 -$1,648,659.38 -$824,329.69 -$412,164.84 -$206,082.42 -$103,041.21 -$51,520.61 -$25,760.30
Income = $0.00 $219,821,250.00 $21,982,125.00 $10,991,062.50 $5,495,531.25 $2,747,765.63 $1,373,882.81 $686,941.41 $343,470.70 $171,735.35 $85,867.68
Total Costs = -$106,178,500.00 -$87,928,500.00 -$6,594,637.50 -$3,297,318.75 -$1,648,659.38 -$824,329.69 -$412,164.84 -$206,082.42 -$103,041.21 -$51,520.61 -$25,760.30
Sum Total = -$106,178,500.00 $131,892,750.00 $15,387,487.50 $7,693,743.75 $3,846,871.88 $1,923,435.94 $961,717.97 $480,858.98 $240,429.49 $120,214.75 $60,107.37
Total Costs with 15% contingency = -$122,105,275.00 -$101,117,775.00 -$7,583,833.13 -$3,791,916.56 -$1,895,958.28 -$947,979.14 -$473,989.57 -$236,994.79 -$118,497.39 -$59,248.70 -$29,624.35
Sum Total with contingency = -$122,105,275.00 $118,703,475.00 $14,398,291.88 $7,199,145.94 $3,599,572.97 $1,799,786.48 $899,893.24 $449,946.62 $224,973.31 $112,486.66 $56,243.33
No Contingency Dollars
NPV @ 13.00% = $32,141,370.18
IRR = 40.271%
Profit = $56,429,117.63
Payback Period ~ 6.53 yrs
With Contingency Dollars
NPV @ 13.00% = $3,154,058.96
IRR = 15.270%
Profit = $25,338,540.42
Payback Period ~ 8.28 yrs

Volume Decline

Volume Decline 0 1 2 3 4 5 6 7 8 9 10 10950000 1095000 547500 273750 136875 68437.5 34218.75 17109.375 8554.6875 4277.34375

Years

Volume (Mscf)

HW 4 Well Data

Cum Volume
2019 75,296
2020 114,613
2021 79,534
2022 54,812
2023 46,212
2024 46,096
2025 38,134
2026 ???
2027 ???
2028 ???

Statistics homework help

Lab Assignment 1

IDS 270

Download data file

The data is located on Blackboard under Week 8 / Lab Assignment 1

Go to Blackboard, right-click on the data file and scroll down to “save target as” or “save link as”.

Save file to Downloads, or wherever you can work with it

2

My Tasks Vs. Your Tasks

The data for this assignment are for reported crimes in Chicago

In hopes that you will find it more interesting vs. generic data sets out there

The instructional material uses data through 2016

The file for you to use on Blackboard uses data through 2017

You are to complete all the tasks with the data on Blackboard that goes through 2017

So you cannot simply copy the images in these instructions and turn them in

Where the instructions call for you to isolate data for 2016 and work only with it, you may use either 2016 or 2017

3

Open Tableau; Click on Text File; Find File & Open

4

After loading the data, click on ‘Sheet 1’ on the bottom left corner

5

Crimes Per Year in Chicago (1)

Go to the Tables tab on the left and Click on ‘Primary type’ and drag it to rows.

This may cause delay the first time you do it.

Should then

Look like this

6

Go to the Tables tab and click on ‘Chicago_Crimes_2011_to_2016.csv(Count)’ and drag it to ‘Text’ that’s located on the Marks box.

Results

7

From Tables tab click and drag ‘Date’ to the columns.

8

Drag ‘Chicago_Crimes_2011_to_2016.csv(Count)’ to color on Marks box.

Results

9

Then, click on the drop down menu next to ‘Automatic’ and instead select ‘Square’

Results

10

Crimes per Month

To start a new visualization add a new worksheet by clicking on the Add Worksheet icon

This will create sheet 2

Click and drag ‘Chicago_Crimes_2011_to_2016.csv(Count)’ to Rows.

11

11

Click and drag ‘Date’ to columns.

Crimes per Month

12

Right click on the drop down menu from ‘Date’ and select Month with the format: May 2015. See next for results

Crimes per Month

13

Crimes per Month

Results

14

To add the line with the average: Go to the ‘Analytics’ tab, Select ‘Average Line’ and drag it into the worksheet and you’ll see the ‘Add a Reference Line’ box appear.

Lastly, drop it into the ‘Table’ square.

Crimes per Month

15

Crimes per Month

Results

16

Location of crimes

Add a new worksheet

Click and drag ‘Chicago_Crimes_2011_to_2016.csv(Count)’ into Rows and ‘Location Description’ into Columns.

17

Location of crimes

Go to the top right corner and click on the ‘Show Me’ tab.

Select ‘Treemaps’

Results

18

Changing Color Scheme– Trickiest Part

If your screen looks like this, then click on Show Me tab

To expose color tab behind.

If already seeing color tab, then OK

19

Location of crimes

To change the treemap colors, right click on the drop down menu of the ‘CNT(Chicago_Crimes_2011_to_2016.csv(Count))’ located to the right.

Select Edit Colors and choose the wanted palette [Red-Gold].

(Chicago_Crime

(Chicago_Crim

20

Location of crimes

Click and drag ‘CNT(Chicago_Crimes_2011_to_2016.csv(Count))’ to Label on the Marks tab.

Results

21

Crimes per District

Add a new worksheet

Drag ‘Chicago_Crimes_2011_to_2016.csv(Count)’ to rows

22

Crimes per District

Locate District variable and right click on its drop-down menu.

Select ‘Convert to dimension’.

(You will see District variable’s symbol to the left of its name changes from green to blue and move up to the first half of the variables list)

Results

23

Crimes per District

Now, you will add ‘District’ to columns (at top of Tableau, as you have done previously)

Click and drag ‘Description’ into Marks—Color

(Select ‘Add all members’ if asked)

Results

24

Map of Crimes per District in 2016

Create New Sheet

Click on the drop down menu from the ‘Latitude’ variable

Go to ‘Change Data Type’

Select ‘Number (decimal)

Again select the drop down menu from ‘Latitude’->’Geographic Role’-> ‘Latitude’

Do the same steps for Longitude but select ‘Longitude’ on last step.

25

Map of Crimes per District in 2016

Drag ‘Longitude’ to columns

Drag ‘Latitude’ to rows

26

Map of Crimes per District in 2016

‘Chicago_Crimes_2011_to_2016.csv(Count)’into ‘Size’ located in the Marks box

27

Map of Crimes per District in 2016

Click and drag ‘District’ into ‘Color’

28

Map of Crimes per District in 2016

Click and drag ‘District’ into ‘Label’ to display the dist. Number in map

29

Map of Crimes per District in 2016

To filter data of year 2016 only: drag ‘Date’ into Filters

->Years->Next->Select ‘2016’ only-> Ok

30

To change how the map looks like, go to ‘Map’-> ‘Background Maps’ ->’Streets’ (the one depicted)

Results

31

District 11 Type of Crimes

Add a new worksheet

‘Chicago_Crimes_2011_to_2016.csv(Count)’ into rows

Drag ‘District’ into Filters -> None-> Select ‘11’ only-> Ok

32

District 11 Type of Crimes

Primary Type into ‘Label’

33

District 11 Type of Crimes

Go to the top right and click ‘Show me’ and select packed bubbles

Results

34

District 11 Type of Crimes

Drag Primary Type into ‘Color’

click Add all members if asked

35

‘Chicago_Crimes_2011_to_2016.csv(Count)’ into ‘Label’

Right click on the ‘[T]CNT(Chicago…)’ to get the drop down menu-> Quick Table Calculation-> ‘Percent of Total’

District 11 Type of Crimes

36

District 11 Type of Crimes(3)

Results

37

District 8 & 11 Weekly Crimes

We are comparing district 8 and 11 since they are the two districts with the most cases of crime

Drag ‘Chicago_Crimes_2011_to_2016.csv(Count)’ into rows

Drag ‘Date’ into columns

38

District 8 & 11 Weekly Crimes

Right click ‘Date’ from columns to get the drop-down menu, select ‘Week number’

39

District 8 & 11 Weekly Crimes

Drag ‘District’ into Filters and select 8 and 11 only

40

District 8 & 11 Weekly Crimes

Drag ‘District’ into Color

41

Percentage of arrests in Chicago

Drag ‘Arrest’ into rows

42

New sheet

Percentage of arrests in Chicago

‘Chicago_Crimes_2011_to_2016.csv(Count)’ into columns

43

Percentage of arrests in Chicago

Go to ‘Show me’-> Pie charts

44

Percentage of arrests in Chicago

To change the size of chart-> Click on the Drop-down menu of ‘Standard’-> Click ‘Entire View’

45

Drag ‘Arrest’ into Label

46

‘Chicago_Crimes_2011_to_2016.csv(Count)’ into Label

47

Right click on drop down menu ‘[T]CNT(Chicago…)’ -> Quick Table Calculation-> ‘Percent of Total’

48

Save as twbx file

49

What to Turn In

Save and then submit your tableau document to the blackboard turn-in slot

Sheets in order as shown here

Crimes by Year and type table

Count of crimes with trendline

Tree map of crime location

Colored graph of crimes by type by district

Colored street map of crimes by district

Bubble chart of crimes by type

Crimes by Week for District 8 & 11

Pie chart of percentage of arrests

50

Statistics homework help

NH1516

Respondent sequence number Gender Age in years at screening Race/Hispanic origin Education level – Adults 20+ Marital status Annual family income Ratio of family income to poverty Weight (kg) Standing Height (cm) Body Mass Index (kg/m**2) Waist Circumference (cm) 60 sec. pulse (30 sec. pulse * 2) Systolic: Blood pres (3rd rdg) mm Hg Diastolic: Blood pres (3rd rdg) mm Hg White blood cell count (1000 cells/uL) Lymphocyte percent (%) Monocyte percent (%) Segmented neutrophils percent (%) Eosinophils percent (%) Basophils percent (%) Lymphocyte number (1000 cells/uL) Monocyte number (1000 cells/uL) Segmented neutrophils num (1000 cell/uL) Eosinophils number (1000 cells/uL) Basophils number (1000 cells/uL) Red blood cell count (million cells/uL) Hemoglobin (g/dL) Hematocrit (%) Mean cell volume (fL) Mean cell hemoglobin (pg) MCHC (g/dL) Red cell distribution width (%) Platelet count (1000 cells/uL) Mean platelet volume (fL) Ever used marijuana or hashish Age when first tried marijuana Used marijuana every month for a year? Age started regularly using marijuana How often would you use marijuana? How many joints or pipes smoke in a day? # days used marijuana or hashish/month Ever used cocaine/heroin/methamphetamine Age first used cocaine Ever used heroin Age first used heroin Ever used methamphetamine Age first used methamphetamine Fasting Glucose (mg/dL) Fasting Glucose (mmol/L) Direct HDL-Cholesterol (mg/dL) Direct HDL-Cholesterol (mmol/L) Insulin (uU/mL) Insulin (pmol/L) Insulin Comment Code Total length of ‘food fast’, hours Total length of ‘food fast’, minutes
83732 1 62 3 5 1 10 4.39 94.8 184.5 27.8 101.1 76 116 62 9.8 23.9 8.2 63.5 4 0.5 2.3 0.8 6.2 0.4 0 4.93 15.2 44.7 90.8 30.8 34 13.9 181 8.3 1 2 1 46 1.19
83733 1 53 3 3 3 4 1.32 90.4 171.4 30.8 107.9 72 134 82 7.3 31.3 9.7 54.8 2.6 1.8 2.3 0.7 4 0.2 0.1 4.89 17.5 49.7 101.8 35.8 35.1 13.4 170 9.6 2 2 101 5.59 63 1.63 17.26 103.56 0 12 2
83734 1 78 3 3 1 5 1.51 83.4 170.1 28.8 116.5 56 136 46 4.4 29.9 9.6 55.8 3.9 0.9 1.3 0.4 2.5 0.2 0 4.18 12.4 37.9 90.8 29.6 32.6 14.7 223 9 84 4.66 30 0.78 11.77 70.62 0 10 27
83735 2 56 3 5 6 10 5 109.8 160.9 42.4 110.1 78 136 70 6.1 17.1 10.3 68.7 3.1 0.9 1 0.6 4.2 0.2 0.1 4.54 12.8 40.1 88.3 28.2 31.9 13.1 280 9.1 2 2 61 1.58
83736 2 42 4 4 3 7 1.23 55.2 164.9 20.3 80.4 76 98 56 4.2 47.1 7.8 44.8 0.2 0.2 2 0.3 1.9 0 0 4.16 12.1 36.5 87.8 29.1 33.2 12.3 275 7.7 1 25 1 25 5 4 30 2 84 4.66 53 1.37 5.42 32.52 0 10 35
83737 2 72 1 2 4 14 2.82 64.4 150 28.6 92.9 64 120 60 6.1 31.7 8.5 56.6 2.8 0.5 1.9 0.5 3.5 0.2 0 4.38 13.4 40.6 92.6 30.5 33 14.1 123 10.1 107 5.93 78 2.02 8.24 49.44 0 12 25
83738 2 11 1 6 1.18 37.2 143.5 18.1 67.5 78 100 56 9 36.8 4.3 56.9 1.7 0.4 3.3 0.4 5.1 0.2 0 4.65 13.7 40 86.2 29.4 34.1 13.2 280 7 43 1.11
83739 1 4 3 15 4.22 16.4 102.1 15.7 48.5 7.8 47.4 7.6 41.9 2.9 0.3 3.7 0.6 3.3 0.2 0 4.15 11.5 33.4 80.5 27.6 34.4 14 223 7.8
83740 1 1 2 77 10.1
83741 1 22 4 4 5 7 2.08 76.6 165.4 28 86.6 66 112 74 3.5 38.2 10.6 39.7 10.3 1.3 1.3 0.4 1.4 0.4 0 5.63 15.4 46.8 83.2 27.3 32.8 13.1 210 7.7 1 15 1 16 4 2 25 2 95 5.27 48 1.24 11.39 68.34 0 9 51
83742 2 32 1 4 1 6 1.03 64.5 151.3 28.2 93.3 74 120 72 8.3 35.4 6.7 56 1.3 0.8 2.9 0.6 4.6 0.1 0.1 4.45 13.1 38.6 86.7 29.4 33.9 12.9 236 7.6 1 18 2 2 28 0.72
83743 1 18 5 15 5 72.4 166.1 26.2 5.8 26.3 10.4 58.7 4.2 0.6 1.5 0.6 3.4 0.2 0 5.4 16 48.3 89.5 29.7 33.2 12.5 269 7 2 2 97 5.38 53 1.37 11.4 68.4 0 10 10
83744 1 56 4 3 3 3 1.19 108.3 179.4 33.6 116 70 180 104 6.1 31.7 8.3 57.6 1.7 0.8 1.9 0.5 3.5 0.1 0 4.6 13.9 42.1 91.5 30.2 33 12.3 146 10.3 1 18 2 1 20 2 2 52 1.34
83745 2 15 3 4 0.86 71.7 169.2 25 88.3 92 106 76 8.5 24.3 6.9 65.2 3.1 0.5 2.1 0.6 5.5 0.3 0 4.38 13.8 40.4 92.2 31.5 34.2 12.4 286 7.2 43 1.11
83746 2 4 5 12 17.7 105 16.1 56.5
83747 1 46 3 5 6 3 0.75 86.2 176.7 27.6 104.3 68 150 92 8.3 23.4 6.4 67 2.2 1 1.9 0.5 5.6 0.2 0.1 5.25 15.2 46.8 89.3 29 32.4 14.2 268 8.2 2 2 44 1.14
83748 1 3 4 6 0.94 17.3 103.6 16.1 52.5
83749 2 17 3 14 3.16 75.9 161.7 29 98.3 80 112 62 9 28.5 7.5 63.3 0.5 0.3 2.6 0.7 5.7 0 0 4.45 12.7 38.7 86.9 28.7 33 12.8 292 8 88 4.88 42 1.09 16 96 0 14 34
83750 1 45 5 2 5 4 1.36 76.2 177.8 24.1 90.1 64 108 74 5.1 42.8 14.2 39.5 2.7 0.9 2.2 0.7 2 0.1 0 5.03 15.4 46.9 93.1 30.5 32.7 13.2 156 9.2 1 21 2 1 1 21 2 1 21 84 4.68 50 1.29 2.86 17.16 0 11 0
83751 2 16 1 4 0.58 51.7 152.6 22.2 74.2 80 106 54 9.1 22.6 12.7 62.1 2.1 0.7 2.1 1.2 5.7 0.2 0.1 4.53 12.4 37.1 82.1 27.4 33.3 15.7 279 9.3 55 1.42
83752 2 30 2 4 6 15 5 71.2 163.6 26.6 90.7 60 104 50 9.8 19.7 6.7 72.4 0.7 0.6 1.9 0.7 7.1 0.1 0.1 4.46 14.3 40.8 91.5 31.9 34.9 13.1 269 7.7 1 14 2 2 67 1.73
83753 1 15 4 8 2.49 71.2 170.5 24.5 76.9 54 124 64 3.8 33.1 10.6 51.5 3.9 1.1 1.3 0.4 2 0.1 0 4.81 14.7 43.6 90.7 30.5 33.6 13.6 224 8.1 103 5.71 48 1.24 5.43 32.58 0 10 29
83754 2 67 2 5 1 6 0.89 117.8 164.1 43.7 123 66 116 76 5.9 37.5 10.6 46.8 4.1 1.2 2.2 0.6 2.8 0.2 0.1 5.22 15.7 45.9 87.8 30.1 34.3 13.2 209 8.2 2 130 7.24 50 1.29 32.89 197.34 0 14 34
83755 1 67 4 5 2 5 2.04 97.4 183.8 28.8 106.3 64 132 78 6.4 32.6 9 56.4 1.6 0.5 2.1 0.6 3.6 0.1 0 4.67 14.8 43.8 93.8 31.6 33.7 12.3 170 9 2 284 15.8 57 1.47 19.05 114.3 0 13 49
83756 1 16 3 7 1.11 60 163.9 22.3 76 68 120 70
83757 2 57 2 1 4 5 0.77 80.5 150.8 35.4 113.5 76 148 58 6.7 26.9 8.4 61.7 2.4 0.8 1.8 0.6 4.1 0.2 0.1 4.65 13.6 40.3 86.6 29.1 33.6 13.4 256 7.6 2 2 398 22.1 43 1.11 5.57 33.42 0 9 45
83758 1 80 3 5 2 9 4.71
83759 2 19 1 7 1.74 100.8 175.4 32.8 104.6 78 108 72 12.8 23.4 6.9 68.5 0.8 0.6 3 0.9 8.8 0.1 0.1 4.72 12.4 38.5 81.7 26.3 32.2 14 382 8.1 2 2
83760 2 3 4 7 1.1 14.6 94.7 16.3 47.5 7.2 53.4 8.4 32.1 5.7 0.6 3.8 0.6 2.3 0.4 0 4.7 12.6 37.9 80.6 26.7 33.2 13 503 6.8
83761 2 24 5 5 5 1 0 61.8 156.4 25.3 79.5 68 104 62 7.7 35.3 7.3 56.3 1 0.3 2.7 0.6 4.3 0.1 0 4.19 12.4 36.9 88.1 29.7 33.7 13.1 230 8.8 2 2 95 5.27 41 1.06 13.23 79.38 0 10 36
83762 2 27 4 4 5 6 2.12 107.9 168.5 38 114.8 76 138 70 8.3 25 3.1 71 0.6 0.4 2.1 0.3 5.9 0 0 4.34 10.8 34.1 78.5 24.9 31.8 12.7 259 8.7 34 0.88
83763 2 2 2 9 1.94 12.1 89.8 15 45.6
83764 1 14 3 15 5 54.8 170.8 18.8 69.8 78 102 60 4.5 41 6.1 49.7 2.3 1 1.8 0.3 2.2 0.1 0 4.85 14.6 41.6 85.8 30 35 12.6 284 8.4 369 20.5 39 1.01 30.1 180.6 0 11 36
83765 2 0 3 9 3.17 5.2
83766 2 10 3 14 3.34 51 160 19.9 76.6 90 112 54
83767 2 54 5 4 3 14 2.99 59 149.9 26.3 88.9 76 128 74 7.9 25.1 6 64 4.2 0.8 2 0.5 5.1 0.3 0.1 4.58 13.9 42.1 91.8 30.2 32.9 13.7 225 8.9 2 2 71 1.84
83768 2 15 3 6 1.09 52.4 158 21 73.6 72 108 62 9.7 26.2 7.8 64.8 1 0.3 2.5 0.8 6.3 0.1 0 4.48 13.9 40.3 90 31.1 34.6 12.8 206 9.7 51 1.32
83769 1 49 5 2 1 10 2.97 72.8 170.7 25 96.6 62 112 68 6.9 42 8.9 40.3 7.8 1.1 2.9 0.6 2.8 0.5 0.1 4.65 14 40.7 87.5 30.2 34.5 12.5 263 7 2 2 29 0.75
83770 1 15 4 4 0.66 48 162 18.3 63.6 60 110 42 5.2 25.8 10.8 60.5 2.3 0.7 1.3 0.6 3.1 0.1 0 5.06 14.6 42.6 84.3 28.9 34.2 13.2 216 8.6 99 5.5 68 1.76 4.33 25.98 0 13 59
83771 2 2 1
83772 2 2 5 5 1.25 15.2 93.8 17.3 50.6 17 28.8 7.3 54 9.6 0.4 4.9 1.2 9.2 1.6 0.1 4.56 12.3 36.3 79.8 27.1 33.9 13.1 471 6.8
83773 2 80 3 3 2 7 3.57 67.7 149.8 30.2 108.4 66 142 68 8.6 54.8 7.4 34.2 3.1 0.6 4.7 0.6 2.9 0.3 0.1 4.46 13.3 40.1 89.9 29.8 33.1 13.8 301 7.4 97 5.38 51 1.32 7.82 46.92 0 10 36
83774 2 13 3 15 4.3 55.9 169.7 19.4 76.8 80 106 72 5.8 38.1 6.9 52 2.5 0.6 2.2 0.4 3 0.1 0 4.38 12.7 37.5 85.7 29.1 33.9 13 261 8.1 51 1.32
83775 2 69 2 1 4 2 0.55 77.7 160.2 30.3 106.8 64 130 60 5.3 34.6 6.4 56.5 2.2 0.5 1.8 0.3 3 0.1 0 4.54 13.5 40.4 88.8 29.8 33.5 13.5 158 8.6 2 38 0.98
83776 2 58 1 5 1 14 3.72 56.6 157.5 22.8 83 70 112 60 6.8 30.7 7.6 57.9 3.2 0.8 2.1 0.5 3.9 0.2 0.1 4.18 13.1 39.2 93.8 31.2 33.4 13.2 241 8 72

Statistics homework help

(Note: For every question you either show your work and/or attach SAS output as evidence. Otherwise you will lose all the points, even your answer is right.)

2. A survey question is distributed to a total of 3214 students about what students’ opinion on are requiring mask mandate on the campus.

Here are the counts for responses: 1665 students responded as agreed, total of 324 responded as strongly agreed with requiring a mask mandate on campus.  A total of 888 students responded as disagreed, 123 strongly disagreed, and 214 students are neural.

1) Construct a summary table and displays count, frequency, and cumulative frequency as appropriate.

2) Interpret it.

3. Serum vitamin E levels for adults are normally distributed mean = 900 g/dL and standard deviation = 350 g/dL.

a. If levels above 1,600 g/dL are considered nearly toxic, the percentage of adults having toxic levels is ___________

b. Ten percent of adults have serum vitamin E levels above _____ g/dL.

5. Summarize the following variables : RIDAGEYR(Age in years at screening), INDFMPIR (Ratio of family income to poverty), BMXWT(Weight (kg)), BMXHT(Standing Height (cm)), BMXWAIST(Waist Circumference (cm)), BMXBMI(Body Mass Index (kg/m**2), BPXSY3(Systolic: Blood pres (3rd rdg) mm Hg), BPXDI3(Diastolic: Blood pres (3rd rdg) mm Hg), LBXHGB(Hemoglobin (g/dL)), LBXGLU(Fasting Glucose (mg/dL)), LBDINSI (Insulin (pmol/L)), and DMDMARTL (Marital status), DMDEDUC2(Education level – Adults 20+), DUQ200(Ever used marijuana or hashish), DUQ240(Ever used cocaine/heroin/methamphetamine), DUQ290(Ever used heroin), DUQ330(Ever used methamphetamine in nh1516 dataset .

(Make sure you add other categorical variables above into the table )

1) Summarize these variables and fill the table below

2) Interpret these summary

Variables

All subjects

(N= )

Age(years)

Mean(SD)

Median (min, max)

Ratio of family income to poverty

Mean(SD)

Median (min, max)

Waist Circumference (cm)

Mean(SD)

Median (min, max)

Body Mass Index (kg/m**2)

Mean(SD)

Median (min, max)

Systolic: Blood pres (3rd rdg) mm Hg

Mean(SD)

Median (min, max)

Diastolic: Blood pres (3rd rdg) mm Hg

Mean(SD)

Median (min, max)

Marital status, n(%)

Married

Widowed

Divorced

Separated

Never Married

Living with partner

4. Make boxplots for BPXSY3(Systolic: Blood pres (3rd rdg) mm Hg), BPXDI3(Diastolic: Blood pres (3rd rdg) mm Hg) by ethnicity, respectively. Compare the trend by and interpret.

5. Make bar graphs for DUQ200(Ever used marijuana or hashish) DUQ200(Ever used marijuana or hashish), DUQ240(Ever used cocaine/heroin/methamphetamine), DUQ290(Ever used heroin), DUQ330(Ever used methamphetamine, respectively. Compare and interpret the trend.

6. You collect information on a random sample of women and obtain estimates on vitamin D exposure. However, the results that you find are different than those conducted at another study site. Should you be concerned? Explain your answer using the concept of sampling variability

Statistics homework help

· No handwritten homework will be accepted. If you use equations, you must also contain a nomenclature.

· Use the HW spreadsheet for homework questions below.

· Clearly state all assumptions. 

· Turn in your Excel HW spreadsheet with your written homework and please have your spreadsheet neatly organized.

1.  You have been asked to design a gathering system with a five well connect package. All five wells are to IP (Initial Production) at the same time. Preliminary engineering work has determined that a ten mile 10″ header along with a six-unit compressor station will be needed to move the new gas production. With the following information provided below, run an economic analysis to determine if the proposed project is viable. If the proposed project is not viable, what recommendations would you make to improve the economic viability of this project? For instance, can the five well connect package stand on its own or will additional volumes need to be added (i.e. third party) to justify the project cost or can you lower your material costs; for example, pipeline cost, compression costs or labor cost (within reason) to make the project economical?

a. Choosing only one of the five wells, use the Arps’ and Duong’s type curve models to determine what type of well you are dealing with, all five wells are assumed to produce from the same formation. For example, is this well unconventional or conventional and clearly state why?

i. Plot the type curve and show the curve in your write-up.

b. You have been given seven years of future production data, see HW 4 excel datasheet, from the producer; however, all projects are required to have a ten-year minimum contract term; therefore, you will need to estimate future production. Use empirical concepts (i.e. type curves or a curve fitting technique of your choosing) to project future gas production for years eight, nine and ten.

i. Plot this curve showing production data and your prediction model.

c. Economic metrics are as follows for this project:

i. Company hurdle rate is 13%

ii. Minimum contract length is 10 years.

iii. Pipeline cost for this area is assumed to be $100,000/in-mile.

iv. Labor cost are assumed to be 30% of year 1 revenue and 30% of subsequent yearly revenue.

v. Six-unit equity compressor station is ~ $13,000,000/station.

vi. Use 20% contingency for cost estimates.

d. Deliverables

i. Using the economic example shown in the lecture 4 slides, and in the HW 4 spreadsheet, to provide a similar economic analysis in spreadsheet form.

ii. Determine the following based on the economic metrics provided in item “c”: minimum cost of service, IRR, NPV @ 13%, payback period, total revenue, total profit and total labor cost over the ten-year period.

iii. Plot a Break-Even Cost Analysis showing the payback period for no contingency and with contingency dollars.

iv. What is the total profit, revenue and labor cost of the project over a ten-year period?

v. If one can reduce all material costs by 10% what is the new IRR and NPV @ 13% with the same cost of service found in d(ii)?

Statistics homework help

INFERENTIAL STATISTICS FOR DECISION MAKING

Chapter-10

Effect Size, Confidence Intervals, and NHST: Two-Sample Designs

Use the following data set to answer the following questions. To earn full credit show all of your calculations and other work. Explain your answers. Don’t just write a number.

The 26 students who signed up for General Psychology reported their GPA. Each person was matched with another person on the basis of the GPAs, and two groups were formed. One group was taught with the traditional lecture method by Professor Nouveau. The other class could access the Web for the same lectures whenever they wished. At the end of the term, both classes took the same comprehensive final exam, and they also filled out a “Satisfaction Questionnaire.” Scores on both measures are shown below.

Analyze the data with t tests and effect size indexes. Write a conclusion.

You have to use the JASP Software (https://jasp-stats.org/download/) to perform your analysis. Make sure you include the analysis output in your submission. Also, explain your results in detail.

Comprehensive Final Exam Scores

Satisfaction

Scores

Traditional Section

Online Section

Traditional Section

Online Section

50

56

25

31

72

75

18

19

64

62

40

38

82

90

31

35

89

91

17

24

65

65

22

20

74

72

14

18

85

87

36

35

80

76

27

31

65

79

22

27

82

77

23

27

75

78

28

28

64

70

20

23

Give examples and elaborate on the applications of the topic.

Chapter-10: Effect Size, Confidence Intervals, and NHST: Two-Sample Designs

1. Describe the following terms: treatments, experimental group, and control group. Give examples and applications.

2. How do you create a paired-sample experiment? Discuss in detail and give examples.

3. What does “Power” mean in an experiment?

1. What factors impact the power of an experiment?

1. The Smiths and McDonalds blame each other for Michael and Jane falling in love. On a test of propensity to fall in love, the mean of 6 members of the Smith family was 54 and the mean of 10 members of the McDonald family was 64. When a statistician compared the families’ scores with a t test, to determine if one family was more at fault, a value of 2.13 was obtained. As a statistician if you adopt an α level of .05 (two-tailed test), what should be your conclusion?

Statistics homework help

Deliverable 07 Worksheet

Scenario

You are currently working at NCLEX Memorial Hospital in the Infectious Diseases Unit. Over the past few days, you have noticed an increase in patients admitted with a particular infectious disease. You believe that the ages of these patients play a critical role in the method used to treat the patients. You decide to speak to your manager, and together you work to use statistical analysis to look more closely at the ages of these patients.

You do some research and put together a spreadsheet of the data that contains the following information:

· Client number

· Infection disease status

· Age of the patient

You need the preliminary findings immediately so that you can start treating these patients. So, let’s get to work!

Background information on the Data:

The data set consists of 70 patients that have the infectious disease with ages ranging from 41 years of age to 84 years of age for NCLEX Memorial Hospital.

Requirements:

1) Answer the questions below in a PowerPoint presentation.

2) Include the summary calculations and the formulas in your slides either symbolically or from Excel. Do not round your results.

3) Show calculations in your Excel spreadsheet.

Submit both the PowerPoint and Excel files.


PowerPoint Presentation Requirements

Slide 1

Title

Title Slide

Slide 2

Overview

Provide a brief overview of the scenario you are given above and the data set that you will be analyzing.

Slide 3

Classification

Classify the variables in your data set.

· Which variables are quantitative/qualitative?

· Which variables are discrete/continuous?

· Describe the level of measurement for each variable included in the data set (nominal, ordinal, interval, ratio)

Slide 4

Measures of Center

What are the measures of center and why are they important? Describe each individually and list any advantages or disadvantages that each may have.

Slide 5

Measures of Variation

What are the measures of variation and why are they important? Describe each individually and list any advantages or disadvantages that each may have.

Slide 6

Calculations

Show your results for the following calculations. Include formulas used in Excel. Interpret your results in the context of the scenario and include units of measurement for each.

· Mean

· Median

· Mode

· Mid-range

· Range

· Variance

· Standard Deviation

Slide 7

Confidence Intervals

Show your responses for the follow questions:

· What are confidence intervals?

· What is a point estimate?

· What is the best point estimate for a population mean? Explain.

· Why do we need confidence intervals?

Slide 8

Confidence Intervals

Construct a
95%
confidence interval for the population mean ages of the patients. Assume that your data is normally distributed and σ is unknown.

Show results for the following calculations in constructing the confidence interval. Include formulas used in Excel. Interpret the confidence interval.

· Critical Value

· Margin of Error

· Upper and Lower Bounds

Slide 9

Hypothesis Testing

Perform the following hypothesis test based on the claim that the average age of all patients admitted to the hospital with infectious diseases is less than 64 years of age.

Write the null and alternative hypothesis symbolically and include the following additional information:

· Which hypothesis is the claim?

· Is the test two-tailed, left-tailed, or right-tailed? Explain

· Which test statistic will you use for your hypothesis test, z-test or t-test? Explain.

Slide 10

Hypothesis Testing

Continue the hypothesis test based on the claim that the average age of all patients admitted to the hospital with infectious diseases is less than 64 years of age.

Show your results and formulas used for the following calculations:

· Test Statistic

· Critical Value

· P-value

Slide 11

Hypothesis Testing

Complete the hypothesis test by explaining the following:

· Decision to reject the null hypothesis or to not reject the null hypothesis.

· Explain your decision using the critical value method.

· Explain your reasoning using the P-value method.

· Restate your conclusion in non-technical terms.

Slide 12

Conclusion

Conclude by recapping your ideas by summarizing the information presented in context of the scenario.

· Include the mean, standard deviation, confidence interval with interpretation, and result of the hypothesis test.

· What conclusions, if any, do you believe we can draw as a result of your study?

· What did you learn from the project about the population based on this sample?

· What did you learn about the specific statistical tests you conducted?

Statistics homework help

attachment_2 (3).docx

Code

Composer/Arranger

Title

Publisher

Grade

Event

Cost

Selling Price

YTD Units Sold

Prior Year Units Sold

BR5016

HUSA

DIVERTIMENTO FOR BRASS & PERCUSSION

AMP

5

BRASS CHOIR

3.25

6.80

42

162

BR5018

MERRIMAN

THEME AND FOUR VARIATIONS

AMP

5

BRASS CHOIR

5.60

8.50

53

53

BR6021

RIEGGER

NONET FOR BRASS

AMP

6

BRASS CHOIR

5.40

9.10

99

72

BU5019

EAST / FROMME

DESPERAVI

AMP

5

BRASS QUINTET

3.25

9.70

64

137

BU6015

HAUFRECHT

SUITE (ANY 2 MVTS)

AMP

6

BRASS QUINTET

5.60

8.10

75

123

FH4029

HANDEL / EGER

SONATA IN G MINOR (MVTS 1&2 OR 3&4)

AMP

4

HORN SOLO

5.50

6.50

13

204

FH5001

ADAMS

LARGO

AMP

5

HORN SOLO

3.25

5.40

55

166

TU3036

SIEKMANN

PARABLE

BAR

3

TUBA SOLO

5.60

8.10

5

204

TU4001

BARNHOUSE

BARBAROSSA

BAR

4

TUBA SOLO

5.20

9.50

58

217

FH4053

SCHULLER

NOCTURNE

BEL

4

HORN SOLO

3.25

6.10

37

14

FH5042

STRAUSS / POTTAG

FANTASIE

BEL

5

HORN SOLO

3.25

9.70

91

81

TB4021

HIDAS

MEDITATION FOR BASS TROMBONE (BASS TBN)

BH

4

TROMBONE SOLO

5.30

5.60

46

31

TB6003

BARTA

KONCERTINO

BH

6

TROMBONE SOLO

5.10

9.80

20

29

BU5051

SMITH

CESARE LA BAVARA

BRP

5

BRASS QUINTET

3.25

9.50

73

55

TP5012

BRAHMS / SAWYER

ANDANTE

BRP

5

TRUMPET SOLO

3.25

5.40

10

46

TP5052

SACHSE / GLOVER / LEWIS

CONCERTINO IN Eb

BRP

5

TRUMPET SOLO

3.25

7.70

67

203

BU6008

BUSS

CONCORD

BX

6

BRASS QUINTET

5.30

5.70

2

73

EU4024

SIMON

WILLOW ECHOES

CF

4

EUPHONIUM SOLO

5.60

7.80

30

130

EU5011

DE LUCA

BEAUTIFUL COLORADO

CF

5

EUPHONIUM SOLO

3.25

5.50

86

63

TU5024

RINGLEBEN

STORM KING

CF

5

TUBA SOLO

3.25

9.00

1

102

TU6001

ARBAN

CARNIVAL OF VENICE

CF

6

TUBA SOLO

5.30

5.70

32

44

BR4018

HOVAHANESS

FANTASY NO 3

CFP

4

BRASS CHOIR

3.25

9.30

17

21

BR4019

HOVAHANESS

FANTASY NO 4

CFP

4

BRASS CHOIR

3.25

5.20

64

149

BR5003

COWELL

RONDO

CFP

5

BRASS CHOIR

3.25

9.10

2

89

BU5029

HOVHANESS

SIX DANCES

CFP

5

BRASS QUINTET

3.25

6.30

64

18

TP6025

LUENING

INTRODUCTION AND ALLEGRO

CFP

6

TRUMPET SOLO

5.60

7.40

40

137

TP7010

STEVENS

SONATA

CFP

7

TRUMPET SOLO

5.40

6.00

13

123

EU5031

VIVALDI / OSTRANDER

CONCERTO IN A MINOR

EM

5

EUPHONIUM SOLO

3.25

6.80

91

72

EU7006

UBER

SONATA FOR EUPHONIUM

EM

7

EUPHONIUM SOLO

5.60

6.70

74

23

FH4046

PURCELL / SMIM

SONATA IN G MINOR (MVT 1)

EM

4

HORN SOLO

3.25

8.10

13

65

FH4048

RAVEL / MAGANINI

PAVANE

EM

4

HORN SOLO

5.10

5.20

94

58

TB5056

SPILLMAN

CONCERTO FOR BASS TROMBONE & PIANO

EM

5

TROMBONE SOLO

3.25

5.20

98

123

EU4009

HANDEL / BARNES

SOUND AN ALARM (JUDAS MACCABEUS)

JS

4

EUPHONIUM SOLO

3.25

9.40

7

47

EU5020

MARTEAU / BARNES

MORCEAU VIVANT

JS

5

EUPHONIUM SOLO

3.25

8.60

36

36

TP3069

SCARLATTI / BARNES

ARIA FROM OPERA TIGRAINE

JS

3

TRUMPET SOLO

5.60

7.00

59

91

TP5062

TELEMANN / BARNES

ARIE FROM PIMPINONE

JS

5

TRUMPET SOLO

5.50

6.20

0

145

BR4040

WAGNER / SCHMIDT

EVENING STAR

KM

4

BRASS CHOIR

3.25

5.50

21

29

BU5044

ROE

MUSIC FOR BRASS QUINTET (ALL MVTS)

KM

5

BRASS QUINTET

5.50

6.60

54

185

BU6005

BACH / FOTE

CONTRAPUNCTUS 9

KM

6

BRASS QUINTET

3.25

6.30

31

62

FH3066

VON WEBER / MUSSER

MARCIA MAESTOSO

KM

3

HORN SOLO

5.10

9.90

85

94

FH3067

WAGNER / UBER

RIDE OF THE VALKYRIES

KM

3

HORN SOLO

3.25

7.70

70

220

TB5042

NESTICO

REFLECTIVE MOOD

KM

5

TROMBONE SOLO

3.25

9.10

38

82

TB6014

DEDRICK

INSPIRATION

KM

6

TROMBONE SOLO

3.25

6.10

43

204

BR6011

HANDEL / DISHINGER

WATER MUSIC SUITE #1

MMP

6

BRASS CHOIR

5.20

5.40

90

131

EU2020

HANDEL / DISHINGER

BOURREE

MMP

2

EUPHONIUM SOLO

3.25

8.60

1

220

EU2021

HANDEL / DISHINGER

SARABANDE

MMP

2

EUPHONIUM SOLO

3.25

8.60

26

184

FH5017

HANDEL / DISHNGER

WATER SUITE MUSIC SUITE NO.2 ( FROM WATER MUSIC SUITE NO. 3)

MMP

5

HORN SOLO

3.25

5.20

91

156

FH5029

MOZART / RAMM

SONATINA #1

MMP

5

HORN SOLO

3.25

7.80

96

66

TB4023

KAPLAN

SOLILOQUY FOR TROMBONE

MMP

4

TROMBONE SOLO

5.40

5.90

63

221

TB4033

MOZART / DISHINGER

CONCERTO IN Eb K.V. 142 (MVT 1 OR 2)

MMP

4

TROMBONE SOLO

5.60

8.40

72

37

TP5019

FITZGERALD

CONCERTINO

MMP

5

TRUMPET SOLO

5.10

5.20

3

168

TP5027

HANDEL / PERRY

SUITE NO 5

MMP

5

TRUMPET SOLO

5.20

9.50

58

23

TU3032

PURCELL / DISHINGER

GAVOTTE AND HORNPIPE

MMP

3

TUBA SOLO

3.25

8.00

11

220

TU3040

TCHAIKOVSKY / GERSHENFELD

AT THE DANCE

MMP

3

TUBA SOLO

5.10

9.80

22

84

BR6013

KABALESKY

SONATINA NO 1

MUS

6

BRASS CHOIR

3.25

6.40

61

63

BR4035

PILSS

HELDEKLAGE

RK

4

BRASS CHOIR

5.40

9.00

60

50

BR4036

PILSS

TWO CHORALES (BOTH MVTS)

RK

4

BRASS CHOIR

5.40

9.20

41

130

TP4035

HAYDN / VOXMAN

ARIA AND ALLEGRO

RU

4

TRUMPET SOLO

3.25

6.70

61

47

TP4056

MOZART / VOXMAN

CONCERT ARIA

RU

4

TRUMPET SOLO

5.00

10.00

55

36

TP5031

HUBANS / VOXMAN

SECOND CONCERTINO

SMC

5

TRUMPET SOLO

5.20

9.50

25

220

TP6016

ERLANGER / ANDRAUD

SOLO DE CONCERT

SMC

6

TRUMPET SOLO

5.20

5.50

33

184

TU6003

BEVERSDORF

SONATA

SMC

6

TUBA SOLO

3.25

9.60

16

95

TU6018

OSMON

CONCERT ETUDES FOR SOLO TUBA (MVTS 7 or 10)

SMC

6

TUBA SOLO

3.25

6.60

98

140

EU4021

PRYOR / SCHIFRIN

CAKEWALK CONTEST

VM

4

EUPHONIUM SOLO

3.25

7.20

42

17

EU5030

UBER

DANZA ESPANA

VM

5

EUPHONIUM SOLO

3.25

6.60

98

111

HQ4023

MCKAY

TWO PIECES

WB

4

HORN QUARTET

3.25

7.30

30

66

HQ5005

HANDEL / SEYMOUR

FUGHETTA OF THE LITTLE BELLS

WB

5

HORN QUARTET

5.50

8.50

15

192

TB3040

KETELBEY / TEAGUE

IN A MONASTERY GARDEN

WB

3

TROMBONE SOLO

5.60

6.70

24

145

TB5027

GUILMANT

MORCEAU SYMPHONIQUE

WB

5

TROMBONE SOLO

5.40

9.20

32

29

EU6016

SIMONE MANITA

BELIEVE ME OF ALL THOSE ENDEARING YOUNG CHARMS

WHAM

6

EUPHONIUM SOLO

5.20

9.40

70

68

TP5057

SMITH

FANTASY FOR TRUMPET

WJ

5

TRUMPET SOLO

3.25

6.40

9

17

TP5058

SMITH

RONDO FOR TRUMPET

WJ

5

TRUMPET SOLO

5.60

7.30

83

111

TU4014

MATTHEWS

ALLELUJA, EXULTATE

WJ

4

TUBA SOLO

3.25

5.60

82

162

TU5008

DANBURG

SONATINA

WJ

5

TUBA SOLO

5.40

6.20

8

53

TU5029

VAUGHAN

CONCERTPIECE NO. 2

WJ

5

TUBA SOLO

3.25

7.10

50

111

attachment_1 (2).pdf

Excel 1 Tutorial Assignment – ISM3011

Ask before/after/during class or come into office/online hours if you have questions on any of this. Refer to the syllabus on
Academic Dishonesty and group/individual work and allowable help for all projects – also remember it’s your responsibility to protect
your work.

Before you start — read this whole assignment and use an optional text and/or review the tutorials as necessary. A project overview
is also available.

Part 1 – Create / Download

• Create a blank workbook. Name it using your Last name followed by your initials and _ 1EX (underscore then 1EX). For
Example: WarnerBL_1EX .xlsx or xls. Either extension is fine

• Copy/paste the data from Excel 1- Music Data.docx , into the 2nd worksheet in your workbook. Name the tab MUSIC.

• Adjust the YTD Units Sold (this represents current sales) and Prior Year Units Sold columns so that their titles are wrapped onto
2 or 3 lines within one cell. Adjust the Title column so that titles can be wrapped on 2 or more lines within one cell as needed
(so titles are not cut-off). See the sorted example below.

• Sort the data (do not sort or remove the title/heading rows) by Code. Check the sort to be sure all is correct.

• Add conditional
formatting to this
Music worksheet
that highlights any
selling prices of $9
or more with a
green background.
If the selling prices
is lowered below
$9, the formatting
should change
automatically.

• Using the named
range feature of
Excel, name all the
cells in this
worksheet,
MusicData.

• No additional data/formulas should be added to the worksheet.

➔ Part 1 Video: https://www.youtube.com/watch?v=-zw4Sdn70xQ

Part 2 – Set up your 1st
worksheet

• Name the tab for the
first worksheet,
LookUp. Below is a
sample of how I set up
my worksheet. Use
your own color scheme
for your project – but
include borders and
backgrounds and
include all of the steps,
as shown below.

Step #1 – Title
o Include a title with your name and any other information you think is appropriate. Merge and center it across all

columns with data.
o Below the title add the current date formula. Be sure you use the appropriate formula so that whenever your

worksheet is opened, the current date is displayed (will change as the date changes). Again use the merge and center
feature.

o Add a colored border to the title and date rows (not black/ blue) & be sure the border is visible on all 4 sides (put a
blank row above the title and a blank column to the left of the title so the whole border can be seen). Include a
background color and font color (besides black/ blue).

o Add a comment or note (using the comment or note feature) to your title and add your name and your email address.

Step #2 – Input Area
o Add an area to enter a music code. Try to make it obvious to the user that this is the data entry area. Use placement,

borders, and/or background colors to distinguish it from the rest of the worksheet.
o Include an arrow in this section; make it a color other than black. Use the SHAPE feature in Excel to create the arrow.

➔ Part 2, Steps 1-2 Video: https://www.youtube.com/watch?v=Np7Mtzynh60

Step #3 – Music Lookup Information
o Use the VLOOKUP function/formula and search the Music worksheet for the code that the user entered in Step 2.
o Display the information for the Code selected – use the same layout as in the example above.

o Note that in the video link below, cell C12 is displayed as currency, it should not be currency.
o Correctly use your named range (MusicData) and absolute cell referencing in your VLOOKUP formulas

Step #4 – Calculations

o Calculate and display the following in the LookUp worksheet. Don’t add any new formulas to the Music worksheet.
o Gross Margin (Markup $)
o Markup Percent based on the cost
o 2016 Goal %: enter 15% into this cell. The goal is a 15% increase from 2015 sales on all music.
o 2016 Goal in Units: calculate the new goal (15% increase from 2015 sales). NOTE: You can’t sell partial units, so

don’t display decimal places – instead use the INT function to round down to the nearest integer.
o Units to meet 2016 goal. How many units need to be sold to meet the 2016 goal? Look at the 2016 goal and the

YTD Units Sold. Use an IF function/formula so that no negative numbers are displayed (if they have sold more than
their goal).

o Using another IF statement, display a message if the sales goal has been met. Use a bright colored font for this
message. If the sales goal has not been met, do not display anything.

o Display the lookup information & calculations in the same order as the example above.

➔ Part 2, Steps 3-4 Video: https://www.youtube.com/watch?v=qN4ABFlXY3o

Step #5 – Graph/Chart

o Create the column chart displayed above:
▪ Select only the data needed for the chart (don’t select all data & delete items from the chart). Do not display any

additional fields.
▪ Display the data values for each column
▪ The title should include the music title and should change each time new information is displayed. It should also

be a larger font (greater than 12) and be a color other than blue or black.
▪ Place the chart on your LookUp worksheet.
▪ Format your chart & include:

▪ a 2-color gradient to format the columns
▪ a colored background on the chart
▪ colored fonts

▪ Do not use dark blue/black for these colors.

➔ Part 2, Step 5 Video: https://www.youtube.com/watch?v=0CVGdWyFq5A

Part 3 – Pivot worksheets

• Using the data in the Music worksheet, create 2 pivot worksheets
o The first should be a pivot table showing each Event Name and the average Selling Price. Format the table so that your

numbers have a dollar sign, two decimal places. Add a title and format it so it looks nice. Name the tab Pivot 1.
o The second should be a pivot table and chart showing each grade level code and the units sold for both years. The numbers

should have commas and no decimal places and include data labels. Add a title and format it so it looks nice. Name this tab
Pivot 2.

o Add one more Pivot worksheet that shows some interesting analytics. Add a textbox to the worksheet to explain what you
are showing. Include a title and nice formatting. Name this tab Pivot 3.

➔ Part 3 Video: https://www.youtube.com/watch?v=BlkSrPBzDDI

Part 4 – Filtering

• Create 3 worksheets and name their tabs Filter1, Filter2 and Filter 3.

• Copy the Music worksheet data into each one of the filter worksheets.

• Filter 1 – display all publishers with the letter K in their code and any events with the word ‘Brass’ in the event name.

• Filter 2 – display Tuba music for grades higher than 3.

• Filter 3 – show some interesting analytics. Add a textbox to the worksheet to explain what you are showing.

➔ Part 4 Video: https://www.youtube.com/watch?v=p_6RvvyvPm0

Part 5 – Finishing Up

• **Use the IFERROR function and if a user enters a MUSIC Code that doesn’t exist, display ‘Code Not Found’ for the title and
blanks for the rest of the cells below. You can let the 15% display, if you’d like (cell C20 in my example).

• **Protect the LookUp worksheet so that the only change a user can make is to enter a different MUSIC Code. They shouldn’t be

able to change any other cells in the worksheet. Don’t use a password, just leave that blank. Don’t guess how to do this, if you
don’t know – watch the Tips on it. Test it when you’re done to be sure we can open the worksheet and enter a new MUSIC
Code and be sure we can’t change any other cells in the worksheet.

• Your worksheets should be in the following order: LookUp, Music, your 3 pivots and then your 3 filter worksheets.
• Once a user enters a new MUSIC Code in the LookUp worksheet, all of the data and chart should automatically change.

• Check your worksheet and be sure there are no errors or error symbols in your finished worksheet. If you don’t have this
feature come into the lab to do this step.

• Check your formatting – currency should have a $ and 2 decimal places, percentages should be formatted with a % sign and 1
decimal place.

• Check your formulas, be sure they are correct and make sense. For example, if you are subtracting 2 numbers don’t use the
SUM formulas (sum is for adding). Excel may figure out what you mean, but we want the formulas to be used correctly (show
that you understand how to use them).

➔ Part 5 Video: https://www.youtube.com/watch?v=3Q7Wkq_sQPA

Project Submission Instructions / Notes:

• Office/online hours get busy as deadlines approach. If you procrastinate and wait until the last days to work on your project,
you may not be able to get all the help you want.

• The only way we can fairly grade the projects is if we check for each requirement. Please go through the instructions before you
submit & be sure you have done each one correctly so you don’t miss out on points. Compare your solution to the project
overview.

• Submitting:

o Remember to leave all of the internal file properties intact for your project, if they are modifi

Statistics homework help

Master List

From Drilling Info.
Well Number Well Name
224020 CHARLENE 4
224023 COULTER HOPPESS TRUST#1
224024 DCR 1
224025 DCR 3
224172 EMBRA #1
224026 GLYNDA 2
224027 HANHART 1
224028 HOYT UNIT 01
224029 HOYT UNIT 02
224030 INGRAM 01

224020

Date Monthly Oil (bbl) Monthly Gas (Mcf) Monthly Water (bbl) Avg Daily Oil (bbl) Avg Daily Gas (Mcf) Avg Daily Water (bbl) Wells Days
Nov-08 0 71,153 626 0 2,372 20.87 1 0
Dec-08 4 1,000,105 8,798 0.13 32,261 284 1 0
Jan-09 0 993,244 8,737 0 32,040 282 1 0
Feb-09 0 915,804 8,056 0 32,707 288 1 0
Mar-09 0 992,222 8,728 0 32,007 282 1 0
Apr-09 0 458,272 4,031 0 15,276 134 1 0
May-09 0 324,946 2,858 0 10,482 92.19 1 0
Jun-09 0 315,017 2,771 0 10,501 92.37 1 0
Jul-09 0 325,486 2,863 0 10,500 92.35 1 0
Aug-09 0 325,093 2,860 0 10,487 92.26 1 0
Sep-09 0 316,101 2,781 0 10,537 92.7 1 0
Oct-09 0 325,695 2,865 0 10,506 92.42 1 0
Nov-09 0 215,544 1,896 0 7,185 63.2 1 0
Dec-09 0 449,689 3,956 0 14,506 128 1 0
Jan-10 0 564,184 4,963 0 18,199 160 1 0
Feb-10 0 485,911 4,274 0 17,354 153 1 0
Mar-10 0 494,399 4,349 0 15,948 140 1 0
Apr-10 2 442,116 3,889 0.07 14,737 130 1 0
May-10 7 410,264 3,609 0.23 13,234 116 1 0
Jun-10 12 377,051 3,317 0.4 12,568 111 1 0
Jul-10 0 349,280 3,073 0 11,267 99.13 1 0
Aug-10 0 321,393 2,827 0 10,368 91.19 1 0
Sep-10 1 299,458 2,634 0.03 9,982 87.8 1 0
Oct-10 0 278,946 2,454 0 8,998 79.16 1 0
Nov-10 0 244,434 2,150 0 8,148 71.67 1 0
Dec-10 0 258,548 2,274 0 8,340 73.35 1 0
Jan-11 0 265,449 2,335 0 8,563 75.32 1 0
Feb-11 1 245,109 2,156 0.04 8,754 77 1 0
Mar-11 0 257,231 2,263 0 8,298 73 1 0
Apr-11 1 228,840 2,013 0.03 7,628 67.1 1 0
May-11 0 180,416 1,587 0 5,820 51.19 1 0
Jun-11 0 139,544 1,228 0 4,651 40.93 1 0
Jul-11 0 110,033 968 0 3,549 31.23 1 0
Aug-11 0 122,591 1,078 0 3,955 34.77 1 0
Sep-11 0 117,826 1,036 0 3,928 34.53 1 0
Oct-11 0 143,084 1,196 0 4,616 38.58 1 0
Nov-11 1 133,764 1,118 0.03 4,459 37.27 1 0
Dec-11 0 136,708 1,143 0 4,410 36.87 1 0
Jan-12 0 129,071 1,079 0 4,164 34.81 1 0
Feb-12 0 116,425 973 0 4,015 33.55 1 0
Mar-12 0 121,606 1,017 0 3,923 32.81 1 0
Apr-12 0 114,735 959 0 3,825 31.97 1 0
May-12 0 119,821 5,022 0 3,865 162 1 0
Jun-12 0 115,156 4,827 0 3,839 161 1 0
Jul-12 0 115,737 4,851 0 3,733 156 1 0
Aug-12 0 117,110 4,909 0 3,778 158 1 0
Sep-12 0 110,717 4,641 0 3,691 155 1 0
Oct-12 0 111,842 1,163 0 3,608 37.52 1 0
Nov-12 2 105,797 1,100 0.07 3,527 36.67 1 0
Dec-12 0 106,178 1,104 0 3,425 35.61 1 0
Jan-13 1 106,791 1,110 0.03 3,445 35.81 1 0
Feb-13 0 92,034 957 0 3,287 34.18 1 0
Mar-13 3 99,825 1,038 0.1 3,220 33.48 1 0
Apr-13 1 96,391 1,002 0.03 3,213 33.4 1 0
May-13 1 98,681 1,026 0.03 3,183 33.1 1 0
Jun-13 3 87,935 955 0.1 2,931 31.83 1 0
Jul-13 0 88,199 958 0 2,845 30.9 1 0
Aug-13 1 82,347 894 0.03 2,656 28.84 1 0
Sep-13 0 82,903 900 0 2,763 30 1 0
Oct-13 0 87,673 952 0 2,828 30.71 1 0
Nov-13 0 90,429 982 0 3,014 32.73 1 0
Dec-13 0 83,754 909 0 2,702 29.32 1 0
Jan-14 0 75,148 816 0 2,424 26.32 1 0
Feb-14 0 72,946 792 0 2,605 28.29 1 0
Mar-14 0 83,535 907 0 2,695 29.26 1 0
Apr-14 0 78,308 850 0 2,610 28.33 1 0
May-14 2 80,895 878 0.06 2,610 28.32 1 0
Jun-14 0 77,536 842 0 2,585 28.07 1 0
Jul-14 0 78,601 853 0 2,536 27.52 1 0
Aug-14 0 76,464 830 0 2,467 26.77 1 0
Sep-14 3 77,258 839 0.1 2,575 27.97 1 0
Oct-14 3 9,383 102 0.1 303 3.29 1 0
Nov-14 1 0 0 0.03 0 0 1 0
Dec-14 1 17 0 0.03 0.55 0 1 0
Jan-15 0 13,515 147 0 436 4.74 1 0
Feb-15 1 25,044 272 0.04 894 9.71 1 0
Mar-15 0 12,944 141 0 418 4.55 1 0
Apr-15 0 10,833 118 0 361 3.93 1 0
May-15 0 18,414 200 0 594 6.45 1 0
Jun-15 0 21,376 232 0 713 7.73 1 0
Jul-15 1 22,869 248 0.03 738 8 1 0
Aug-15 0 29,921 325 0 965 10.48 1 0
Sep-15 0 27,313 297 0 910 9.9 1 0
Oct-15 1 28,137 305 0.03 908 9.84 1 0
Nov-15 1 26,392 287 0.03 880 9.57 1 0
Dec-15 0 27,485 298 0 887 9.61 1 0
Jan-16 0 26,949 293 0 869 9.45 1 0
Feb-16 0 26,709 290 0 921 10 1 0
Mar-16 0 30,078 327 0 970 10.55 1 0
Apr-16 1 27,435 298 0.03 915 9.93 1 0
May-16 0 28,958 314 0 934 10.13 1 0
Jun-16 0 28,481 309 0 949 10.3 1 0
Jul-16 1 28,747 312 0.03 927 10.06 1 0
Aug-16 1 29,482 320 0.03 951 10.32 1 0
Sep-16 0 26,700 290 0 890 9.67 1 0
Oct-16 0 31,070 337 0 1,002 10.87 1 0
Nov-16 0 29,472 320 0 982 10.67 1 0
Dec-16 1 30,128 327 0.03 972 10.55 1 0
Jan-17 1 28,962 314 0.03 934 10.13 1 0
Feb-17 0 26,529 288 0 947 10.29 1 0
Mar-17 1 28,717 312 0.03 926 10.06 1
Apr-17 1 27,801 302 0.03 927 10.07 1
May-17 28,816 313 930 10.1 1
Jun-17 1 26,735 290 0.03 891 9.67 1
Jul-17 1 26,636 289 0.03 859 9.32 1
Aug-17 1 27,309 296 0.03 881 9.55 1
Sep-17 1 26,666 290 0.03 889 9.67 1
Oct-17 27,143 295 876 9.52 1
Nov-17 28,613 311 954 10.37 1
Dec-17 30,835 335 995 10.81 1
Jan-18 1 34,949 379 0.03 1,127 12.23 1
Feb-18 2 35,724 388 0.07 1,276 13.86 1
Mar-18 40,513 440 1,307 14.19 1
Apr-18 1 40,304 438 0.03 1,343 14.6 1
May-18 1 40,691 442 0.03 1,313 14.26 1
Jun-18 38,038 413 1,268 13.77 1
Jul-18 41,246 448 1,331 14.45 1
Aug-18 1 41,818 454 0.03 1,349 14.65 1
Sep-18 2 42,913 466 0.07 1,430 15.53 1
Oct-18 42,785 464 1,380 14.97 1
Nov-18 42,497 461 1,417 15.37 1
Dec-18 25,913 281 836 9.06 1
Jan-19 39,318 427 1,268 13.77 1
TABLE

224023

Statistics homework help

Epidemic Models

SIRS Model

In this set of notes, we will talk about SIR models, which are the standard for of model for infectious diseases.
We will follow the steps outlined in the Introduction to Modeling notes:

1. Understand the question.

2. Translate the biological question into a mathematical question via assumptions.

3. Formulate the model that will answer the question.

4. Run/analyze the model.

5. Use the model results to answer the question.

6. Evaluate the reliability of the results.

What do we want to know about epidemics?

We will focus on three questions:

1. What characteristics of a disease make it spread widely and become an epidemic? What is different
between epidemic diseases and non-epidemic ones?

2. Why do epidemics often exhibit cycles in number of infected individuals?

3. When do epidemics end?

Assumptions of the SIR model

In an SIR model, we assume that everyone in the population is in one of three categories: suspectible to the
disease, infected by the disease, or recovered from the disease. Susceptibles are people who have not had the
disease and who can be infected by it. Infecteds are people who currently have the disease. Depending on the
disease, there may be a risk of mortality while infected. Recovered means that the person had the disease
and have now recovered from it. The term SIR refers to Susceptible-Infected-Recovered.
For many diseases, a person has immunity once they have recovered and thus cannot get the disease again.
In this case, a person who has recovered will not ever return to the susceptible status. However, with some
diseases the immunity can disappear with time and thus people can return to the susceptible status. In this
case, the model is called SIRS (Susceptible-Infected-Recovered-Susceptible)

1

Image from institutefordiseasemodeling.github.io

In order to formulate a mathematical model, we need be more precise about how we think the disease will
work. Take S as the number of susceptibles, I as the number of infecteds, R as the number of recovereds,
and N as the total population size (i.e. N = S + I + R). We will start with the following assumptions:

1. All population members can be placed into one of three categories: susceptible to the disease, infected
by the disease, or recovered from the disease.

2. Susceptible individuals become infected by contact with infected ones. The rate of infection is propor-
tional to the rate of contact between susceptibles and infecteds. That is βSI, where β is a constant
that determines how infectious the disease is.

3. Infected individuals recover at rate γ. Individuals in the recovered status cannot become infected.

4. Recovered individuals become susceptible again at rate ξ.

5. For now, we will assume no vital dynamics. That is, no birth or death. This means that the disease
does not cause mortality and the time scale is short enough that changes in population size are not
significant.

Formulate the Model

The basic SIR model is known as a compartment model. A compartment model describes how materials
of some kind are transmitted between different compartments or states. In an SIR model, the materials
are people (or other organisms) in the population. The compartments are the disease states of susceptible,
infected, and recovered. The model describes how people move through these states over time.

We will use system of differential equations to formulate the model:

dS

dt
= −βSI + ξR

dI

dt
= βSI −γI

dR

dt
= γI − ξR

dS
dt
, dI
dt
dR
dt

are the rate of change in the number of susceptible, infected, and recovered individuals, respectively.
The right hand side of each equation quantifies how the value changes depending on the other values. That is,

(Change in Number of Susceptibles)=(loss of susceptibles to infection)+(gain from recovereds that turn
susceptible)

2

(Change in Number of infecteds)=(gain from susceptiblels due to infection)+(loss from infecteds that recover)

(Change in Number of recovereds)=(gain of recovereds from infecteds)+(loss from recovereds that turn
susceptible)

Question: Consider the total population size N = S + I + R. How does it change with time? How can we tell?

Analyze the Model

We will have to take a long detour to learn how to analyze the model. This is a set of ordinary differential
equations (ODE).These are nonlinear ODEs because the right hand side is not linear in the variables.

Ideally, we would like to solve these equations and get expressions for S(t), I(t), and R(t).

Unfortunately, systems of non-linear ODEs do not generally have analytic solutions (that is, solutions that we
can write down in explicit mathematical form). Some special cases can be solved, but we usually have to solve
them numerically – that is, use a computer to approximate solutions. We will first talk about equilibrium
solutions to the model and then talk about using an R package to solve them numerically.

Equilibrium behavior of the SIRS Model

A common strategy for gaining insight into ODE models is finding the equilibrium behavior. Typically, an
ODE model will have short term transient behavior that depends on the initial conditions and will eventually
settle into long-term steady state behavior.

In the steady state, the numbers of infecteds, recovereds, and susceptibles are not changing. Thus, we can
find this steady state behavior by setting the derivatives equal to zero and solving for S, I, and R:

dS

dt
= 0 ⇒−βSI + ξR = 0 ⇒

SI

R
=
ξ

β

dI

dt
= 0 ⇒ (βS −γ)I = 0

dR

dt
= γI − ξR ⇒ I = R

γ

ξ

Note also that

S + I + R = N

This gives equations in the three unknowns (S,I,R) that we can solve.

The second equation is zero either if I = 0 or S = γ
β
In the I=0 case we can see from the third equation that

R=0 also. Then, we have

S̄ = N − I −R = N

In this case, the disease has died out. There are no infected individuals and no recovered ones. The entire
population is susceptible.

3

In the other solution, we have
S̄ =

γ

β
.

The third equation gives

R̄ = Ī
ξ

γ

Then, we have
S̄ + Ī + R̄ = N

or
γ

β
+ Ī + Ī

ξ

γ
= N

Solving for Ī, we get

Ī = γ
N − γ

β

γ + ξ
and

R̄ = Ī
ξ

γ
= ξ

N − γ
β

γ + ξ

To summarize, we have

S̄ =
γ

β

Ī = γ
N − γ

β

γ + ξ

R̄ = ξ
N − γ

β

γ + ξ

In this solution, the epidemic goes to an equilibrium with a constant number of susceptibles, infecteds, and
recovereds in the population. This does not mean that the individuals are constant in one of the states.
Rather, there are always people moving between the three states (S ⇒ I ⇒ R), but the numbers in each
state are in equilibrium with the rate of flow of individuals between the states.

To summarize, we have seen that this model has two steady states:

(S̄1, Ī1) = (N, 0)

(S̄2, Ī2) = (
γ

β
,
ξ
(
N − γ

β

)(
γ + ξ)

) )
One steady state in which the disease dies out and one in which it becomes endemic in the population. In
order for the second steady state to exist (i.e. be non-negative), we must have

4

N >
γ

β

If this condition is not met and N < γ
β
, then only the steady state (N, 0) exists. In this case, the disease

will die out of the population. More formal methods (beyond the scope of this class) demonstrate that this
condition is key to the dynamics of the model.

If the condition is not met, typical dynamics will look like:

0 20 40 60 80 100

1
2

0
1

3
0

1
4

0
1

5
0

S

time

0 20 40 60 80 100

0
1

0
2

0
3

0
4

0
5

0

I

time

If the condition N > γ
β
is met, then disease will persist. This condition is commonly expressed as

R0 =

γ
> 1

R0 is called the intrinsic reproductive rate of the disease. This is the average number of individuals that will
be infected by an infected individual. β is the infection rate and γ is the average time to recovery from the
disease. Thus, β

γ
is the fraction of the population that is infected by an infected individual during the period

of infection. If this greater than one, then the disease will persist.

In this case, both steady states exist, but only the upper one is stable. That the (N, 0) steady state exists
means that if there is no infected individuals in the population then the system will remain in that state of
having no infecteds. That this steady state is unstable means that if any infecteds are introduced into the
population (that is, we move a short distance off of the steady state), then the disease will spread until the
equilibrium is reached at the other steady state. Typical dynamics look like

5

0 50 100 150 200

1
6

0
2

0
0

2
4

0
2

8
0

S

time

0 50 100 150 200
2

5
3

0
3

5
4

0
4

5
5

0

I

time

Answering our first question of interest

This gives us the key to answering our first question of interest:

What characteristics of a disease make it spread widely and become an epidemic? What is
different between epidemic diseases and non-epidemic ones?

R0 is the key quantity in determining how widely a disease will spread in the population in its early stages.

R0 =

γ

Here are estimated values of R0 for several pandemics:

6

image from https://www.the-scientist.com/features/why-r0-is-problematic-for-predicting-
covid-19-spread-67690

The determinants of R0 are

β: New individuals become infected at rate βSI. S and I are the number of susceptible and infected
individuals. β is impacted by the behavior of the hosts and the properties of the disease:
Behavior: The more contact between susceptible and infected individuals, the higher the rate of transmission.
Disease infectiousness: The mechanics of disease transmission determine how readily the disease transmits in
a given situation.

γ: The longer the infectious period, the more disease transmission will occur.

Evaluate the reliability of the results.

Class discussion: How reliable do you think that our model is? Can you identity any problems
with it?

Submit your answer to eLC.

7

Numerically Solving Systems of Ordinary Differential Equations:

Consider our SIR Model:

dS

dt
= −βSI + ξR

dI

dt
= βSI −γI

dR

dt
= γI − ξR

Ideally, we would like to solve this find functions S(t),I(t),R(t) that would tell us the number of Susceptibles,
Infecteds, and Recovereds at any time t. Unfortunately, it is not usually possible to solve non-linear systems
of ODEs. We can solve linear system, but usually not non-linear ones. In a linear system, the right hand
side would involve only linear functions of the variables (that is, all terms would either be a constant or a
constant multiplied by a single variable)

There are two common approaches to nonlinear ODES: numerical solutions andqualitative analysis. A
numerical solution means using a computer program to give approximate solutions over specified times ranges.
Qualitative analysis means using mathematical techniques to find out the big picture of how the solutions
behave, without actually explicitly solving the ODEs.

We are not going to talk about the mathematics of how numerical ODE solvers work. Rather, we are simply
going to apply an ODE solve in R and look at the results. We will use an R package deSolve.

We will need to install the deSolve package in order to use it. You can do this by going to the Tools menu
at the top of the R studio window. Click Tools>Install Packages…, then enter deSolve under Packages
and click Install. This will install the package on your computer. You then must use the library command
to load it.

Within the deSolve package, there is a function called odethat will use to solve the ODEs. Instructions for
using the package are at

https://cran.r-project.org/web/packages/deSolve/vignettes/deSolve.pdf

Read this to see how to use the package.
library(deSolve)

parameters<-c(beta=0.002,xi=0.2,gamma=0.4) #specify model parameters
state<-c(S=990,I=10,R=0) #initial state of the population

SIRmodel<-function(t,state,parameters)
{

with(as.list(c(state,parameters)),{

dS=-beta*S*I+xi*R
dI=beta*S*I-gamma*I
dR=gamma*I-xi*R

return(list(c(dS,dI,dR)))

})
}

8

times<-seq(from=0,to=50,by=0.01)

SIRout<-ode(y=state,times=times,func=SIRmodel,parms=parameters)

par(oma=c(0,0,3,0))
plot(SIRout)
mtext(outer=TRUE,side=3,paste(“SIR model:”,”beta=”,parameters[1],”, xi=”,parameters[2],”, gamma=”,parameters[3], “, R0=”,sum(state)*parameters[1]/parameters[2]))

0 10 20 30 40 50

2
0

0
1

0
0

0

S

time

0 10 20 30 40 50

0
4

0
0

I

time

0 10 20 30 40 50

0
4

0
0

R

time

SIR model: beta= 0.002 , xi= 0.2 , gamma= 0.4 , R0= 10

The population starts with 990 susceptibles and 10 infecteds. It goes through some short term dynamics and
then settles into a steady state with 200 susceptibles, 267 infecteds, and 533 recovereds.

Recall the condition for persistance of the disease:

R0 =

γ
> 1

In this example, we have
(R0=1000*0.002/0.2)

## [1] 10

This is greater than 1, so the disease persists in the population. Let’s do another example where this isn’t
true. We will lower the rate of infection to β = 0.0001. Now, we have
(R0=0.0001/0.2)

## [1] 5e-04

9

Now, the intrinsic reproductive rate of the disease is less than 1. That is, each infected individual will on
average infect less than one other person. We expect the disease to die out:
parameters<-c(beta=0.0001,xi=0.2,gamma=0.4) #specify model parameters
state<-c(S=990,I=10,R=0) #initial state of the population

SIRout<-ode(y=state,times=times,func=SIRmodel,parms=parameters)

par(oma=c(0,0,3,0))
plot(SIRout)
mtext(outer=TRUE,side=3,paste(“SIR model:”,”beta=”,parameters[1],”, xi=”,parameters[2],”, gamma=”,parameters[3], “, R0=”,sum(state)*parameters[1]/parameters[2]))

0 10 20 30 40 50

9
9

0
1

0
0

0

S

time

0 10 20 30 40 50

0
6

I

time

0 10 20 30 40 50

0
3

6

R

time

SIR model: beta= 1e−04 , xi= 0.2 , gamma= 0.4 , R0= 0.5

As expected, the disease dies out and the population is entirely composed of susceptibles. Let’s look at a few
more examples:
parameters<-c(beta=0.0004,xi=0.2,gamma=0.4) #specify model parameters
state<-c(S=990,I=10,R=0) #initial state of the population
times<-seq(from=0,to=5000,by=0.01)

SIRout<-ode(y=state,times=times,func=SIRmodel,parms=parameters)

par(oma=c(0,0,3,0))
plot(SIRout)
mtext(outer=TRUE,side=3,paste(“SIR model:”,”beta=”,parameters[1],”, xi=”,parameters[2],”, gamma=”,parameters[3], “, R0=”,sum(state)*parameters[1]/parameters[2]))

10

0 1000 3000 5000

9
7

5
1

0
0

0

S

time

0 1000 3000 5000

0
6

I

time

0 1000 3000 5000

0
1

0

R

time

SIR model: beta= 4e−04 , xi= 0.2 , gamma= 0.4 , R0= 2

In this example, R0 is only a small distance above 1. The disease does persist, but at a very low level. In
fact, we can’t even tell that is is non-zero in the figure. To be sure, let’s look at the actual numerical output
tail(SIRout) #this shows the last few lines of SIRout

## time S I R
## [499996,] 4999.95 999.5089 0.1636002 0.3275223
## [499997,] 4999.96 999.5089 0.1635998 0.3275217
## [499998,] 4999.97 999.5089 0.1635995 0.3275211
## [499999,] 4999.98 999.5089 0.1635992 0.3275204
## [500000,] 4999.99 999.5089 0.1635989 0.3275198
## [500001,] 5000.00 999.5089 0.1635986 0.3275191

We see that the equlibirum value of I is about 0.16. Of course, we can’t really have fractional individuals.
Thus, this is shortcoming of the model. In reality, the disease would die out at this low level of infectivity.

Note that this plot has a much longer time scale than the previous ones.

Next, we will increase β so that R0 = 4:
parameters<-c(beta=0.0008,xi=0.2,gamma=0.4) #specify model parameters
state<-c(S=990,I=10,R=0) #initial state of the population
times<-seq(from=0,to=50,by=0.01)

SIRout<-ode(y=state,times=times,func=SIRmodel,parms=parameters)

par(oma=c(0,0,3,0))
plot(SIRout)

11

mtext(outer=TRUE,side=3,paste(“SIR model:”,”beta=”,parameters[1],”, xi=”,parameters[2],”, gamma=”,parameters[3], “, R0=”,sum(state)*parameters[1]/parameters[2]))

0 10 20 30 40 50

5
0

0
1

0
0

0

S

time

0 10 20 30 40 50

5
0

2
0

0

I

time

0 10 20 30 40 50

0
2

5
0

R

time

SIR model: beta= 8e−04 , xi= 0.2 , gamma= 0.4 , R0= 4

Now, the steady state has a much higher proportion of infecteds and recovereds.

Increase β to 50:
parameters<-c(beta=0.01,xi=0.2,gamma=0.4) #specify model parameters
state<-c(S=990,I=10,R=0) #initial state of the population

SIRout<-ode(y=state,times=times,func=SIRmodel,parms=parameters)

par(oma=c(0,0,3,0))
plot(SIRout)
mtext(outer=TRUE,side=3,paste(“SIR model:”,”beta=”,parameters[1],”, xi=”,parameters[2],”, gamma=”,parameters[3], “, R0=”,sum(state)*parameters[1]/parameters[2]))

12

0 10 20 30 40 50

0
8

0
0

S

time

0 10 20 30 40 50

0
6

0
0

I

time

0 10 20 30 40 50

0
4

0
0

R

time

SIR model: beta= 0.01 , xi= 0.2 , gamma= 0.4 , R0= 50

Now, the steady state situation is that most of the population is either infected or recovered. Very few are
susceptible.

Finally, let’s decrease ξ to 0.01. This is decreasing the rate at which recovereds become susceptible so that it
rarely happens. Now, most of the population is recovered at any given time. This situation is typical of many
viruses that we commonly encounter. That is, most of the population has previously been exposed and is no
longer susceptible.
parameters<-c(beta=0.01,xi=0.01,gamma=0.4) #specify model parameters
state<-c(S=990,I=10,R=0) #initial state of the population

SIRout<-ode(y=state,times=times,func=SIRmodel,parms=parameters)

par(oma=c(0,0,3,0))
plot(SIRout)
mtext(outer=TRUE,side=3,paste(“SIR model:”,”beta=”,parameters[1],”, xi=”,parameters[2],”, gamma=”,parameters[3], “, R0=”,sum(state)*parameters[1]/parameters[2]))

13

0 10 20 30 40 50

0
8

0
0

S

time

0 10 20 30 40 50

0
6

0
0

I

time

0 10 20 30 40 50

0
6

0
0

R

time

SIR model: beta= 0.01 , xi= 0.01 , gamma= 0.4 , R0= 1000

Phase Plane Diagrams of ODEs

Phase plan diagrams are another useful tool for analyzing systems of ODEs. A phase plan diagram shows the
trajectories of the system at different combinations of the model variables.

We will use the R package PhaseR to plot flow fields for systems of ODEs. This package is designed to be
compatible with deSolve. We will consider the example system

dx

dt
= xy −y

dy

dt
= xy −x

Here is the code:
library(phaseR)

## Warning: package ‘phaseR’ was built under R version 4.0.5

## ——————————————————————————-
## phaseR: Phase plane analysis of one- and two-dimensional autonomous ODE systems
## ——————————————————————————-
##
## v.2.1: For an overview of the package’s functionality enter: ?phaseR
##
## For news on the latest updates enter: news(package = “phaseR”)

14

#function to define the system of equations:

ODE1<-function(t,y,parameters)
{

x<-y[1]
y<-y[2]

dy<-numeric(2)
dy[1]=x*y-y
dy[2]=x*y-x

return(list(dy))
}

ODEflow<-flowField(ODE1,xlim=c(-2,2),ylim=c(-2,2),NULL,add=FALSE,main=”flow field for example system”)

ODENullclines<-nullclines(ODE1,xlim=c(-2,2),ylim=c(-2,2),NULL)

ODETrajectory<-trajectory(ODE1,y0=matrix(c(-2,-1,-1,0,2,0,0,1.5,-1,-2,1.25,1.25,-1,-1.5,1,1.2,0.5,1,1.25,1,1,0.75,0.75,0.5,0.7,0.7),nrow=13,byrow=T),tlim=c(0,2))

## Note: col has been reset as required

−2 −1 0 1 2


2


1

0
1

2

flow field for example system

x

y

x nullclines
y nullclines

15

The function flowfield creates the plot with the arrows. The arrows show the direction of flow of the system
at each (X,y) point. The parameters xlim and ylim define the area of the plot.

The function nullcline adds in the nullclines.These are explained below.

The function trajectory adds curves that show how the system changes with time starting from a specified
point. I have the argument y0 gives the collection of starting points for the trajectories (e.g. the first point is
(-2,-1) and the second point is (-1,0)). The argument tlim specifies how much time the trajectory should be
plotted for. For example, the black curve starting at (-2,-1) shows the trajectory starting from (x,y)=(-2,-1)
and going for 2 time units.

The direction of flow at each point is determined by the values of the derivatives of the model at that point.
Take the point (x = −1,y = −1). The derivatives are

dx

dt
= xy −y = (−1) ∗ (−1) − (−1) = 2

dy

dt
= xy −x = (−1)(−1) − (−1) = 2

Thus, the vector of derivatives is (dx
dt
, dy
dt

) = (2, 2). The vector (2, 2) points in the direction 45 degrees. Note
that this is the direction of the arrow at (−1,−1) in the plot. Similarly, at (x = 1.5,y = −1),we have

dx

dt
= xy −y = (1.5) ∗ (−1) − (−1) = −1.5 + 1 = −0.5

dy

dt
= xy −x = (1.5)(−1) − (1.5) = −3

The vector of derivatives is (dx
dt
, dy
dt

) = (−0.5,−3). We see that the arrow at $(1.5,-1) is pointing more
downwards but a little to the left.

Next, we will find the nullclines. These are lines along which one of the derivatives is equal to zero. Consider
our ODEs. If we set the derivatives to zero, we get

dx

dt
= xy −y = 0 =⇒ xy = y =⇒ x = 1,y = 0

dy

dt
= xy −x = 0 =⇒ xy = x =⇒ x = 0,y = 1

That is dx
dt

= 0 when x = 1 or y = 0 and dy
dt

= 0 when x = 0 or y = 1. The lines corresponding to these values
are shown on the plot: dark blue for x and light blue for y. Note in the plot that the arrows are horizontal
along the light blue line and vertical along the dark blue line.

Where these lines cross, both derivatives are equal to zero and thus there are steady states. This occurs at
(x = 0,y = 0), (1, 1). There are no arrows at these points.

The arrows point away from the point (1, 1). This means that this point is an unstable state. Let’s test this
with the ODE solver:
parameters<-c() #specify model parameters
state<-c(x=1.1,y=1.1) #initial state of the population
times<-seq(from=0,to=10,by=0.01)

ODEmod1<-function(t,state,parameters)
{

16

with(as.list(c(state,parameters)),{

dx=x*y-y
dy=x*y-x

return(list(c(dx,dy)))

})
}

ODEout<-ode(y=state,times=times,func=ODEmod1,parms=parameters)

## DLSODA- Warning..Internal T (=R1) and H (=R2) are
## such that in the machine, T + H = T on the next step
## (H = step size). Solver will continue anyway.
## In above message, R1 = 2.39789, R2 = 1.94531e-16
##
## DLSODA- Warning..Internal T (=R1) and H (=R2) are
## such that in the machine, T + H = T on the next step
## (H = step size). Solver will continue anyway.
## In above message, R1 = 2.39789, R2 = 1.94531e-16
##
## DLSODA- Warning..Internal T (=R1) and H (=R2) are
## such that in the machine, T + H = T on the next step
## (H = step size). Solver will continue anyway.
## In above message, R1 = 2.39789, R2 = 1.61137e-16
##
## DLSODA- Warning..Internal T (=R1) and H (=R2) are
## such that in the machine, T + H = T on the next step
## (H = step size). Solver will continue anyway.
## In above message, R1 = 2.39789, R2 = 1.61137e-16
##
## DLSODA- Warning..Internal T (=R1) and H (=R2) are
## such that in the machine, T + H = T on the next step
## (H = step size). Solver will continue anyway.
## In above message, R1 = 2.39789, R2 = 1.61137e-16
##
## DLSODA- Warning..Internal T (=R1) and H (=R2) are
## such that in the machine, T + H = T on the next step
## (H = step size). Solver will continue anyway.
## In above message, R1 = 2.39789, R2 = 1.28813e-16
##
## DLSODA- Warning..Internal T (=R1) and H (=R2) are
## such that in the machine, T + H = T on the next step
## (H = step size). Solver will continue anyway.
## In above message, R1 = 2.39789, R2 = 1.28813e-16
##
## DLSODA- Warning..Internal T (=R1) and H (=R2) are
## such that in the machine, T + H = T on the next step
## (H = step size). Solver will continue anyway.
## In above message, R1 = 2.39789, R2 = 1.06701e-16

17

##
## DLSODA- Warning..Internal T (=R1) and H (=R2) are
## such that in the machine, T + H = T on the next step
## (H = step size). Solver will continue anyway.
## In above message, R1 = 2.39789, R2 = 1.06701e-16
##
## DLSODA- Warning..Internal T (=R1) and H (=R2) are
## such that in the machine, T + H = T on the next step
## (H = step size). Solver will continue anyway.
## In above message, R1 = 2.39789, R2 = 1.06701e-16
##
## DLSODA- Above warning has been issued I1 times.
## It will not be issued again for this problem.
## In above message, I1 = 10
##
## DLSODA- At current T (=R1), MXSTEP (=I1) steps
## taken on this call before reaching TOUT
## In above message, I1 = 5000
##
## In above message, R1 = 2.39789
##
par(oma=c(0,0,3,0))
plot(ODEout)

0.0 0.5 1.0 1.5 2.0

0
2

0
6

0
1

0
0

x

time

0.0 0.5 1.0 1.5 2.0

0
2

0
6

0
1

0
0

y

time

18

#mtext(outer=TRUE,side=3,paste(“SIR model:”,”beta=”,parameters[1],”, xi=”,parameters[2],”, gamma=”,parameters[3], “, R0=”,sum(state)*parameters[1]/parameters[2]))

We started at (x = 1.1,y = 1, 1) – slightly off of the (x = 1,y = 1) equilibrium. We see that from this point
the system goes away from (1, 1) towards positive x and positive y. This is what we expect if the equilibrium
is unstable. If we try any other points around (x = 1,y = 1) we will find the same thing – that the system
will move away from the equilibrium.

Next, Let’s look at the point (x = 0,y = 0). First, start at (x = 0,y = 0):
parameters<-c() #specify model parameters
state<-c(x=0.5,y=0.5) #initial state of the population
times<-seq(from=0,to=10,by=0.01)

ODEmod1<-function(t,state,parameters)
{

with(as.list(c(state,parameters)),{

dx=x*y-y
dy=x*y-x

return(list(c(dx,dy)))

})
}

ODEout<-ode(y=state,times=times,func=ODEmod1,parms=parameters)

par(oma=c(0,0,3,0))
plot(ODEout)

19

0 2 4 6 8 10

0
.0

0
.1

0
.2

0
.3

0
.4

0
.5

x

time

0 2 4 6 8 10
0

.0
0

.1
0

.2
0

.3
0

.4
0

.5

y

time

#mtext(outer=TRUE,side=3,paste(“SIR model:”,”beta=”,parameters[1],”, xi=”,parameters[2],”, gamma=”,parameters[3], “, R0=”,sum(state)*parameters[1]/parameters[2]))

We see that the system goes to the equilibrium at (x = 0,y = 0). Note that the arrow at (x = 0.5,y = 0.5)
points towards (x = 0,y = 0). However, if we start at (x = 0,y = 0.5), the system ends up on the y = 1
nullcline and then heads to x = −∞.
parameters<-c() #specify model parameters
state<-c(x=0,y=0.5) #initial state of the population
times<-seq(from=0,to=10,by=0.01)

ODEmod1<-function(t,state,parameters)
{

with(as.list(c(state,parameters)),{

dx=x*y-y
dy=x*y-x

return(list(c(dx,dy)))

})
}

ODEout<-ode(y=state,times=times,func=ODEmod1,parms=parameters)

20

par(oma=c(0,0,3,0))
plot(ODEout)

0 2 4 6 8 10


1

0
0

0
0


6

0
0

0

2
0

0
0

x

time

0 2 4 6 8 10

0
.5

0
.6

0
.7

0
.8

0
.9

1
.0

y

time

#mtext(outer=TRUE,side=3,paste(“SIR model:”,”beta=”,parameters[1],”, xi=”,parameters[2],”, gamma=”,parameters[3], “, R0=”,sum(state)*parameters[1]/parameters[2]))

Adding birth and death to the model

One key factor that our model does not include is the possibility of birth and death. Ignoring birth and death
is reasonable if 1) the disease does not cause mortality (or possibly lowe mortality) and 2) the time scale of
the dynamics is short enough that the population size won’t change significantly during the course of the
epidemic.

Now, we will introduce birth and death into the model. Let µ and ν represent the birth and death rates,
respectively. ν is the “background” mortality that occurs in absence of the disease.

We assume

1. birth and death rates are balanced (µ = ν), so that the population size will remain constant.

2. All newborns are in the susceptible class. This is true for many diseases, but not all. For example, HIV
can be passed from the mother to the baby in utero.

3. For now, we will assume that the disease does not cause mortality. Thus, the three classes in the model
(S,I,R) have the same death rate.

Then, the model is

21

dS

dt
= µN −βSI + ξR−νS

dI

dt
= βSI −γI −νI

dR

dt
= γI − ξR−νR

New susceptibles enter the system by birth. Individuals in all three classes leave the system by death.

System Dynamics

Here is the model for the function ode:
SIRmodelBD<-function(t,z,parameters)
{#SIRS model with vital dynamics

beta=parameters[1]
xi=parameters[2]
gamma=parameters[3]
N=parameter

Statistics homework help

Daily Test Question Chapter 5

· Section 5.1: pp. 112, problems #1- #14

1. In your own words, explain why random variables are important to statistics and probability.

2. What is the difference between a continuous and discrete random variable?

3. Would you consider the temperature outside a discrete random variable? Why or why not?

4. Suppose a piggy bank contains 100 coins (25 pennies, 25 dimes, 25 nickels, and 25 quarters). Let the random variable X represent the total value of five randomly selected coins. Is X a discrete or continuous random variable?

5. What are the properties of a continuous distribution?

6. What are the properties of a discrete distribution?

7. Give an example of a discrete and a continuous random variable.

8. Give examples of three different discrete random variables.

9. Give examples of three different continuous random variables.

10. Can you describe a random variable Y that is both discrete and continuous?

11. Suppose you have a dataset and define the random variable X as the number of students at your university with the same last name. what type of random variable is this?

12. Give two examples of variable that are not random.

13. What are the major differences between discrete and continuous random variables?

14. In each of the following situations, indicate whether the random variable is discrete or continuous:

a. The number of Twitter followers for each student in your statistic class

b. The amount of rainfall in 2020 in each U.S. state

c. The amount of time it takes each student in your statistics class to travel to campus

d. The number of text message students on a college campus received today

e. The GPA of the first-year students at your college

· Section 5.2: pp. 114-115, problems #1- #9

1. For discrete random variables, what type of plot would you use to graphically display the probability of distribution? What provides the probability for a specific outcome?

Use the following to answer questions 2-5:

Let’s define an experiment in which a fair coin is tossed three times. Let the random variable X represent the number of times the coin lands on tails in the three flips.

2. What is the probability that two tails are observed?

3. Describe two formulations that you could use to calculate the probability that at least one tail is observed and then solve either.

4. What is the probability that no tails are observed?

5. Create a probability histogram that graphically displays the probability distribution of X.

6. For continuous random variables, what type of plot would you use to graphically display the probability distribution? How is the plot used to find the probability of an event?

7. When visually examining graphs of continuous distributions, what features of the graph are important to notice? What can we note about the area under the entire graph?

8. Consider the continuous probability distribution shown in the graph below. What features of the distribution do you observe?

9. Consider the continuous probability distribution shown in the graph below. What features of the distribution do you observe?

Chart, line chart, histogram  Description automatically generated

Chart, line chart  Description automatically generated

· Section 5.3: pp. 117-118, problems #1- #10

Use the following to answer questions 1-5:

Assume the distribution of a random variable Y is defined in the table below:

A picture containing chart  Description automatically generated

1. Is the distribution a valid probability model? Explain why or why not.

2. Does the probability model describe a continuous or discrete random variable?

3. Compute the central tendency of the probability distribution.

4. What is the variance of the probability distribution?

5. What is the standard deviation of the probability distribution?

Use the following to answer 6-10:

Construct your own valid probability model that describes a discrete random variable X. Assume the random variable X can take on five different values. The random variable X should have an expected value of 12.

6. Fill in the table below to show the values and probabilities for your model.

A picture containing background pattern  Description automatically generated

7. How do you know that you constructed a valid probability distribution?

8. What is the variance of your probability distribution?

9. What is the standard deviation of your probability distribution?

10. Plot the probability histogram.

· Section 5.4: pp. 121, problems #1- #15

1. Is the geometric distribution discrete or continuous?

2. Is the Poisson distribution discrete or continuous?

3. Suppose you flip a coin 10 times and count the number of times the coin lands on heads. Is this a setting that would allow the use of a Poisson distribution?

4. NetflixTM is a popular streaming service that allows you to watch movies and TV shows for a subscription price. Suppose you count the number of episodes each student in your class watched last night of any show. Would this be a setting appropriate for the Poisson distribution? Explain why or why not.

5. Give an example of a dataset that could be modeled using a Poisson distribution.

6. Suppose a couple would like to start having children. The random variable X represents the number of children they have until the first girl. Is this setting for a geometric distribution? Explain why or why not.

7. Give an example of a dataset that could be modeled using the geometric distribution.

Use the following to answer questions 8-10

We are going to use the Poisson distribution to model the number of customers at a popular fast-food chain restaurant. Suppose the mean number of people at the restaurant is 98 during any given hour.

8. What is the probability that there will be over 100 customers at the restaurant from p.m. -6 p.m. today?

9. What is the probability that there will be exactly 10 customers at the restaurant for the hour starting at 1 p.m.?

10. What is the variance for this distribution?

Use the following to answer questions 11-13.

The University of Maryland has approximately 40,000 students from all over the world. As a new student on campus, you are interested in meeting students from your home town of Paris, France. Suppose that when you meet someone, the probability that they are from Paris is .04. Use the geometric distribution to answer the questions below.

11. What is the probability of success, p, and the probability of failure, q, for this distribution?

12. What is the probability you have to ask random students on campus where they are from before you find a student who is from Paris?

13. What is the mean and variance of this distribution?

14. Stephen Curry, a member of the Golden State Warriors professional basketball has one of the three best free throw shooting percentages of all time. Using the fact that his free throw shooting percent is 90.56%, calculate the probability that it takes more than 10 shots before Curry would miss a shot.

15. Babe Ruth, known as The Sultan of Swat, is often referred to as the greatest baseball player of all time. Ruth was known for hitting home runs. He had a career home run percent of 8.5%. Design an appropriate probability model, and then calculate (a) the expected number of at bats to hit a homerun and (b) the probability that Ruth goes more than 15 at bats in a row without a home run.

Statistics homework help

Downloading Tableau

For Lab Assignment 1

IDS 270

You Will Need to Install Tableau on Your PC

Follow the link to get the 14-day trial of Tableau

https://nam04.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.tableau.com%2Fproducts%2Fdesktop%2Fdownload%3Futm_campaign%3DTFT%2520License%2520and%2520Online%2520-%2520Confirmation%2520-%2520Student%2520Lab%2520-%2520Text%26utm_medium%3DEmail%26utm_source%3DEloqua%26domain%3Duic.edu%26eid%3DCTBLS000005942998%26elqTrackId%3Db6f625c3dcd348ddbb836a2dc3280528%26elq%3D75dbc57edf324dd080483e3cd6ce3eaa%26elqaid%3D24643%26elqat%3D1%26elqCampaignId%3D&data=04%7C01%7Cjspark4%40uic.edu%7C90e75822d7c64fdf62d008d97ed5d4a3%7Ce202cd477a564baa99e3e3b71a7c77dd%7C0%7C0%7C637680279127503289%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=Vsp500VMaNGTtXdxRz%2BWWisgriafsc2BJglXq2PF3dI%3D&reserved=0

Tableau Will Download Automatically

Downloaded without

having to ask

Version for Mac also available

Open The Exe File, Check the Boxes, Click on Install

Might Require Re-Boot; Save Your Files First!

Fill In Fields and Click Register

Registration may take a few minutes

That’s It!

Tableau should be work-able

Your screen won’t look exactly like

mine because I have some Tableau

files on my hard drive

Use Open Text File, Open Crime Data (After Download that Crime Data)

Now can definitely go to

next presentation and video

Statistics homework help

· No handwritten homework will be accepted. If you use equations, you must also contain a nomenclature.

· Use the HW Excel spreadsheet for homework questions below.

· Clearly state all assumptions. 

· Turn in your Excel HW spreadsheet with your written homework and please have your spreadsheet neatly organized.

1. You have been asked to look at a grouping of wells, a ten total well package, and you have been asked to develop type curves for each of the ten wells from information that you received from Drilling Info. You are only interested in the gas production and will ignore both crude and water for this exercise.

a. Develop ten type curves using the Arps’ Model?

b. Develop ten type curves using the Duong Model?

c. Describe the differences between the models?

d. What is the error difference between the models?

e. From your results, what can you ascertain about the wells (i.e. are the wells conventional or unconventional)?

f. Which empirical model would you use to represent the wells that you plan to design a gas gathering system around?

g. Choose the best Arps’ Model and Duong Model and post the graphical results below.

2. Develop two probabilistic type curves using the results from the Arps’ and Duong Models.

a. Use the procedure laid out in the lecture slides and attach your results to this document.

b. Develop a production forecast model using the best type curve from exercise one for both Arps’ and Duong Models.

c. Develop a production forecast model using the probabilistic type curves that you have found.

d. What observations can you make from both methods?

Statistics homework help

All that is left is some of 3-1 MyStatLab: Module Three Homework, 5-2 MyStatLab: Midterm Exam, some of 9-2 MyStatLab: Module Nine Homework and 10-1 MyStatLab: Final Exam are you able to assist with these four most of 9 and 3 is done just need some help on getting some passing grade

Statistics homework help

BMX1516

Date Monthly Oil (bbl) Monthly Gas (Mcf) Monthly Water (bbl) Avg Daily Oil (bbl) Avg Daily Gas (Mcf) Avg Daily Water (bbl) Wells Days
Dec-09 0 426,933 3,869 0 13,772 125 1 0
Jan-10 0 613,541 5,560 0 19,792 179 1 0
Feb-10 0 551,821 5,000 0 19,708 179 1 0
Mar-10 0 609,108 5,519 0 19,649 178 1 0
Apr-10 3 597,795 5,417 0.1 19,927 181 1 0
May-10 0 569,851 5,164 0 18,382 167 1 0
Jun-10 4 436,443 3,955 0.13 14,548 132 1 0
Jul-10 0 363,631 3,295 0 11,730 106 1 0
Aug-10 1 247,770 2,245 0.03 7,993 72.42 1 0
Sep-10 2 232,564 2,107 0.07 7,752 70.23 1 0
Oct-10 0 239,470 2,170 0 7,725 70 1 0
Nov-10 0 196,255 1,778 0 6,542 59.27 1 0
Dec-10 0 237,012 2,148 0 7,646 69.29 1 0
Jan-11 0 227,410 2,061 0 7,336 66.48 1 0
Feb-11 1 184,079 1,668 0.04 6,574 59.57 1 0
Mar-11 0 128,766 1,167 0 4,154 37.65 1 0
Apr-11 0 152,681 1,383 0 5,089 46.1 1 0
May-11 0 152,582 1,383 0 4,922 44.61 1 0
Jun-11 0 140,784 1,276 0 4,693 42.53 1 0
Jul-11 0 151,608 1,374 0 4,891 44.32 1 0
Aug-11 0 145,476 1,318 0 4,693 42.52 1 0
Sep-11 0 136,300 1,235 0 4,543 41.17 1 0
Oct-11 0 154,057 1,396 0 4,970 45.03 1 0
Nov-11 0 71,050 644 0 2,368 21.47 1 0
Dec-11 0 132,205 1,198 0 4,265 38.65 1 0
Jan-12 1 125,867 1,141 0.03 4,060 36.81 1 0
Feb-12 0 113,449 1,028 0 3,912 35.45 1 0
Mar-12 0 102,312 927 0 3,300 29.9 1 0
Apr-12 0 49,736 451 0 1,658 15.03 1 0
May-12 0 105,213 4,968 0 3,394 160 1 0
Jun-12 0 98,208 4,637 0 3,274 155 1 0
Jul-12 0 92,386 4,362 0 2,980 141 1 0
Aug-12 0 98,018 4,628 0 3,162 149 1 0
Sep-12 0 84,894 4,009 0 2,830 134 1 0
Oct-12 0 89,407 914 0 2,884 29.48 1 0
Nov-12 2 85,992 879 0.07 2,866 29.3 1 0
Dec-12 0 85,409 873 0 2,755 28.16 1 0
Jan-13 1 83,112 850 0.03 2,681 27.42 1 0
Feb-13 0 74,617 763 0 2,665 27.25 1 0
Mar-13 0 81,459 833 0 2,628 26.87 1 0
Apr-13 2 77,449 792 0.07 2,582 26.4 1 0
May-13 0 77,208 805 0 2,491 25.97 1 0
Jun-13 0 66,579 694 0 2,219 23.13 1 0
Jul-13 0 66,539 694 0 2,146 22.39 1 0
Aug-13 0 35,118 366 0 1,133 11.81 1 0
Sep-13 0 64,187 669 0 2,140 22.3 1 0
Oct-13 1 66,810 697 0.03 2,155 22.48 1 0
Nov-13 0 59,327 619 0 1,978 20.63 1 0
Dec-13 1 76,095 793 0.03 2,455 25.58 1 0
Jan-14 1 70,044 730 0.03 2,259 23.55 1 0
Feb-14 1 54,117 564 0.04 1,933 20.14 1 0
Mar-14 0 60,495 631 0 1,951 20.35 1 0
Apr-14 0 73,418 766 0 2,447 25.53 1 0
May-14 1 71,324 744 0.03 2,301 24 1 0
Jun-14 0 12,363 129 0 412 4.3 1 0
Jul-14 0 41,620 434 0 1,343 14 1 0
Aug-14 0 55,603 580 0 1,794 18.71 1 0
Sep-14 2 56,791 592 0.07 1,893 19.73 1 0
Oct-14 2 60,570 632 0.06 1,954 20.39 1 0
Nov-14 2 67,975 709 0.07 2,266 23.63 1 0
Dec-14 1 65,669 685 0.03 2,118 22.1 1 0
Jan-15 0 38,582 402 0 1,245 12.97 1 0
Feb-15 2 60,077 626 0.07 2,146 22.36 1 0
Mar-15 1 52,359 546 0.03 1,689 17.61 1 0
Apr-15 1 63,679 664 0.03 2,123 22.13 1 0
May-15 0 64,027 668 0 2,065 21.55 1 0
Jun-15 1 53,275 556 0.03 1,776 18.53 1 0
Jul-15 1 75,439 787 0.03 2,434 25.39 1 0
Aug-15 0 67,163 700 0 2,167 22.58 1 0
Sep-15 1 55,851 582 0.03 1,862 19.4 1 0
Oct-15 1 60,777 634 0.03 1,961 20.45 1 0
Nov-15 1 55,800 582 0.03 1,860 19.4 1 0
Dec-15 1 51,051 532 0.03 1,647 17.16 1 0
Jan-16 0 62,316 650 0 2,010 20.97 1 0
Feb-16 1 63,920 667 0.03 2,204 23 1 0
Mar-16 0 63,149 658 0 2,037 21.23 1 0
Apr-16 1 40,544 423 0.03 1,351 14.1 1 0
May-16 0 42,039 438 0 1,356 14.13 1 0
Jun-16 1 51,750 540 0.03 1,725 18 1 0
Jul-16 2 43,912 458 0.06 1,417 14.77 1 0
Aug-16 3 36,172 377 0.1 1,167 12.16 1 0
Sep-16 1 57,267 597 0.03 1,909 19.9 1 0
Oct-16 1 40,174 419 0.03 1,296 13.52 1 0
Nov-16 0 23,252 242 0 775 8.07 1 0
Dec-16 3 2,658 28 0.1 85.74 0.9 1 0
Jan-17 2 0 0 0.06 0 0 1 0
Feb-17 1 16,866 176 0.04 602 6.29 1 0
Mar-17 2 39,169 408 0.06 1,264 13.16 1
Apr-17 2 39,298 410 0.07 1,310 13.67 1
May-17 1 52,963 552 0.03 1,708 17.81 1
Jun-17 1 25,819 269 0.03 861 8.97 1
Jul-17 1 40,969 427 0.03 1,322 13.77 1
Aug-17 1 27,482 287 0.03 887 9.26 1
Sep-17 2 43,530 454 0.07 1,451 15.13 1
Oct-17 44,183 461 1,425 14.87 1
Nov-17 34,649 361 1,155 12.03 1
Dec-17 3,334 35 108 1.13 1
Jan-18 1 34,485 360 0.03 1,112 11.61 1
Feb-18 2 33,903 354 0.07 1,211 12.64 1
Mar-18 35,124 366 1,133 11.81 1
Apr-18 2 23,659 247 0.07 789 8.23 1
May-18 1 40,666 424 0.03 1,312 13.68 1
Jun-18 25,679 268 856 8.93 1
Jul-18 1 34,758 362 0.03 1,121 11.68 1
Aug-18 1 37,972 396 0.03 1,225 12.77 1
Sep-18 2 25,391 265 0.07 846 8.83 1
Oct-18 5,668 59 183 1.9 1
Jan-19 591 6 19.06 0.19 1
Nov-17 28,613 311 954 10.37 1
Dec-17 30,835 335 995 10.81 1
Jan-18 1 34,949 379 0.03 1,127 12.23 1
Feb-18 2 35,724 388 0.07 1,276 13.86 1
Mar-18 40,513 440 1,307 14.19 1
Apr-18 1 40,304 438 0.03 1,343 14.6 1
May-18 1 40,691 442 0.03 1,313 14.26 1
Jun-18 38,038 413 1,268 13.77 1
Jul-18 41,246 448 1,331 14.45 1
Aug-18 1 41,818 454 0.03 1,349 14.65 1
Sep-18 2 42,913 466 0.07 1,430 15.53 1
Oct-18 42,785 464 1,380 14.97 1
Nov-18 42,497 461 1,417 15.37 1
Dec-18 25,913 281 836 9.06 1
Jan-19 39,318 427 1,268 13.77 1

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Statistics homework help

1.1

31. Marriage Proposals In a survey conducted by 

TheKnot.com

, 1165 engaged or married women were asked about the importance of a bended knee when making a marriage proposal. Among the 1165 respondents, 48% said that the bended knee was essential.

a. What is the exact value that is 48% of 1165 survey respondents?

b. Could the result from part (a) be the actual number of survey subjects who said that a bended knee is essential? Why or why not?

c. What is the actual number of survey respondents saying that the bended knee is essential?

d. Among the 1165 respondents, 93 said that a bended knee is corny and outdated. What percentage of respondents said that a bended knee is corny and outdated?

1-2#

In 
Exercises 21

28
, determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate.

22. Exit Poll For the presidential election of 2016, ABC News conducts an exit poll in which voters are asked to identify the political party (Democratic, Republican, and so on) that they registered with.

Statistics homework help

Project #1 – STAT 4660
Fall 2022

Due Friday March 4 by midnight

In this this project you will conduct a simulation study of different COVID mitigation strategies and
use it to make a case for what you think the best strategy would have been. You will simulate a town of
population approximately 10,000 people for several years (or however long it takes for the epidemic to
run its course). In your town, people should live in households with other people and go to work or
school. This will allow you to model disease transmission dynamics in a more realistic way than the
previous models that we have studied. You should have a moderately realistic structure to your town in
terms of household composition and number and size of businesses. You introduce the disease into the
town in a small number of individuals and then see how the disease spreads. You should test at least the
following scenarios:

1) No mitigation strategies are attempted.
2) Total lockdown with no one leaving home.
3) Lockdowns with e.g. 90%, 80%, …50%,… of people staying home.
4) Measures such as masking and social distancing. You can model these simply as reductions in

transmission probabilities.
5) School closing only. Businesses stay open.
6) Businesses only closing. Schools stay open.
7) You should consider these scenarios with and without a vaccine.

You should consider metrics such as total deaths, total cases, number of people with long
COVID, etc. It might make sense to consider not just deaths, but years of life lost (i.e. a child dying is
many more years of life lost than an 80-year-old and this is relevant).
The various parameters in your model should be based on real data. This includes:

– Household composition (i.e. number of households with one person, two people, two people
with kids, how many kids, etc).

– Infection rates in different settings: home, school, work.
– Mortality rates by age.
– Length of time that someone is infectious.
– Probability of long COVID.
You should write a report that explains what you did, your results with figures/tables, and your

conclusions about the best COVID strategy.
In order to get a good grade, you must do the following:
– Clearly explain your assumptions (i.e. the rules of how your simulation works).
– Make a reasonable effort to have realistic assumptions.
– Have a thorough discussion of caveats and shortcomings of your model and results.
– Have your code match your stated assumptions.
– Have your model parameters based on data and reference the source of that data.
– Have code that is well organized and documented.
– Have appropriate figures and tables.
– Make a good case for your preferred mitigation strategy based on model output. We are

modeling the disease side of things in detail, but not modeling things like economic impacts, lost

education opportunities, mental health impacts, etc. Thus, you can make qualitative arguments
about these things.

Hints:
1. Your program should follow the same basic form as the IBM model in the lecture notes. That is,

there should be a matrix or data frame that tracks the state of the population, with rows
corresponding to members of the population and columns corresponding to variables that you
want to track. There should be a loop over time and in each time step various functions are
applied to the population that implement processes such as infection, recovery, etc.

2. My population data frame has columns of disease status, age, age at infection, sex, household
index, workplace/school, employee index/school grade, day of recovery if infected, day of
death if they die from disease, indicator long COVID. My program does not actually use age at
infection or sex, but I kept these from the previous program in case I want them in the future.
You do not need to have exactly the same columns. I am telling you this to give an example of
what I did.

3. You should make a function to construct your population. You will need to do this many times
and you will want to experiment with different population compositions. Having a function will
make this more convenient. My function is of form make_households(F0,nw,sb,lb,nsb,nlb),
where F0 is the number of households, nw is the number of people who don’t work, sb is the
number of small businesses with nsb employees, and lb is the number of large businesses with
nlb employees. The function loops over desired households. For each one, it randomly
determines the household composition (single individual, couple, couple with kids, etc) and the
number of children (if there are any) based on real data for the US. I have another function that
takes the values nw,sb,lb,nsb, and nlb and constructs the available jobs. It then randomly
assigns adults to jobs. It does similarly with schools for children. It calculates grade in school
based on age.

4. Households, jobs, and schools only matter in the model because they determine which
members of the population interact with each other and therefore can infect each other. Rates
of infection may vary between different settings.

5. I have separate functions for disease transmission in households, businesses, schools, and in the
community. I also have a functions that implement mitigation measures such as lockdowns.
Putting things in functions allows you to easily change them in the future. For example, if I
decide that I want to have household disease transmission work in a different way, it just means
writing a new function. Provided that the input and output is the same, I don’t need to change
anything else in the program.

6. There are many different pieces to this program, but work on one thing at a time. Keep testing
as you go along. Check at every step to make sure that your code is doing what it is supposed to.

7. The first thing that you probably should do is the make the function that constructs your
population because you can’t test anything else until you have a correct population data frame.

8. You will get most of the data for model parameters from scientific papers. One way to find these
is using Google Scholar. Search “scholar” on Google and it will give you Google Scholar. E.g.
searching “us household composition” led me to the data on which I based my
make_households function.

9. One advantage of using functions is that you can start with parameter values that you make up
for testing and then easily plug in better values later after doing research.

10. There is partial credit! Your program does not have to be perfect to get points.

Statistics homework help

DEMO1516

Respondent sequence number Weight (kg) Standing Height (cm) Body Mass Index (kg/m**2) Waist Circumference (cm)
83732 94.8 184.5 27.8 101.1
83733 90.4 171.4 30.8 107.9
83734 83.4 170.1 28.8 116.5
83735 109.8 160.9 42.4 110.1
83736 55.2 164.9 20.3 80.4
83737 64.4 150 28.6 92.9
83738 37.2 143.5 18.1 67.5
83739 16.4 102.1 15.7 48.5
83740 10.1
83741 76.6 165.4 28 86.6
83742 64.5 151.3 28.2 93.3
83743 72.4 166.1 26.2
83744 108.3 179.4 33.6 116
83745 71.7 169.2 25 88.3
83746 17.7 105 16.1 56.5
83747 86.2 176.7 27.6 104.3
83748 17.3 103.6 16.1 52.5
83749 75.9 161.7 29 98.3
83750 76.2 177.8 24.1 90.1
83751 51.7 152.6 22.2 74.2
83752 71.2 163.6 26.6 90.7
83753 71.2 170.5 24.5 76.9
83754 117.8 164.1 43.7 123
83755 97.4 183.8 28.8 106.3
83756 60 163.9 22.3 76
83757 80.5 150.8 35.4 113.5
83759 100.8 175.4 32.8 104.6
83760 14.6 94.7 16.3 47.5
83761 61.8 156.4 25.3 79.5
83762 107.9 168.5 38 114.8
83763 12.1 89.8 15 45.6
83764 54.8 170.8 18.8 69.8
83765 5.2
83766 51 160 19.9 76.6
83767 59 149.9 26.3 88.9
83768 52.4 158 21 73.6
83769 72.8 170.7 25 96.6
83770 48 162 18.3 63.6
83772 15.2 93.8 17.3 50.6
83773 67.7 149.8 30.2 108.4
83774 55.9 169.7 19.4 76.8
83775 77.7 160.2 30.3 106.8
83776 56.6 157.5 22.8 83
83777 69 166.1 25 93.5
83778 99.9 170.2 34.5 111.5
83779 11.8
83780 18.2 103.9 16.9 54.5
83781 87.8 160.7 34 103.6
83783 96.4 171.1 32.9 107
83784 73.7 170.7 25.3 86.2
83785 75.6 145.2 35.9 108
83786 102.1 182.2 30.8 107.7
83787 77.4 152 33.5 103.1
83788 84 164.6 31 103
83789 102.9 173.9 34 109.5
83790 85.6 187.4 24.4 100.5
83791 78.6 167.6 28 104.2
83792 17.4 103.8 16.1 53.4
83793 56.3 157.7 22.6 78
83794
83795 23 120.2 15.9 55.4
83796 20.3 102.6 19.3 57.5
83797 9.8
83798 8.2
83799 66.6 161.6 25.5
83800 34.7 141.8 17.3 59.4
83801 58.5 157.1 23.7 90.1
83802 68.4 169.8 23.7 93
83803 79.1 166.3 28.6 93.7
83804 12.6
83805 41.5 139.4 21.4 68.4
83806 15.3 90.8 18.6
83807 47.3 150.1 21 68.8
83808 21.9 112.3 17.4 53.6
83809 72.9 166.8 26.2 92.6
83810 24 121 16.4 53.6
83811 27.9 123.4 18.3 57.2
83812 63.7 147.9 29.1 110
83813 89.2 182.2 26.9 89.2
83814 41.4 143.4 20.1 68.2
83815 80.9 159.1 32 103
83816 59.3 178.4 18.6 79.1
83817 86.1 183.7 25.5 96.8
83818 72.3 159.2 28.5 97.9
83819 78.3 156.2 32.1 109.9
83820 81.7 173.8 27 100.3
83821 79.8 165.7 29.1
83822 60.4 164.8 22.2 78.4
83823 66.8 150 29.7 96.5
83824 72.4 180.3 22.3 80.7
83825 55.6 160.5 21.6 78
83826 21.8 107.6 18.8 61.3
83827 93 177.5 29.5 109.4
83828 71.3 162 27.2 94.6
83829 65.8 170.6 22.6 90
83830 77.2 175.5 25.1 78.8
83831 92.2 173.9 30.5 98.3
83832 105.9 157.7 42.6 129.1
83833 50.7 169.3 17.7 66.5
83834 87.7 176.4 28.2 105.3
83835 79.4 163.2 29.8 101.8
83836 68.6 156.5 28 89.3
83837 77.5 148.3 35.2 107.6
83838 34.3 134.1 19.1 73
83839 53.8 171.6 18.3 72.9
83840 7.3
83841 55.9 164.6 20.6 73.6
83842
83843 78.3 179.7 24.2 104.5
83844 68.9 172.8 23.1 85.2
83845 133.3 171.5 45.3
83847 71.2 185 20.8 77.8
83848 44.6 143 21.8 77.1
83849 80.3 170.6 27.6 101.7
83851 85.1 155.3 35.3 106.5
83852 7.2
83853 76.1 166.7 27.4 88.7
83854 110.2 162.7 41.6 110.2
83855 33.6 143.9 16.2 58.5
83856 89.1 181.5 27 99.1
83857 70.4 159 27.8 85
83858 7.5
83859 11.8 88.2 15.2 45.7
83860 146.1 189.4 40.7 134.6
83862 60.3 157.1 24.4 78.7
83863 95.8 175.6 31.1 104.6
83864 19.5 111.6 15.7 54.1
83865 39.7 156.3 16.3 65.5
83866 88 169.3 30.7 93
83867 72.3 173.9 23.9 83
83868 43.2 145.7 20.4 71
83869 61.3 160.2 23.9 94.3
83870 82.4 169.8 28.6 94.2
83871 53.7 139.9 27.4 82.4
83872 67.2 170 23.3 88.9
83873 17.8 104.8 16.2 54.1
83874 91.2 173.9 30.2 97.1
83875 91.6 163.1 34.4 99.4
83876 61.5 152.7 26.4
83878 42.2 151.2 18.5 64
83879 50.3 150.5 22.2 71.4
83880 49.7 143.9 24
83881 63.2 162.7 23.9 80.3
83882 21 112.7 16.5 54.4
83883 46.7 152.4 20.1 78.4
83884 62.2 167 22.3 86.5
83885 48.7 149.3 21.8 74.5
83886 84.1 175.9 27.2 102.8
83887 51.4 149.3 23.1 74
83888 15.7 99.1 16 51.1
83889 77.7 178.7 24.3 94.2
83890 50.5 157.4 20.4 69.3
83891 109.5 167.9 38.8 111.1
83892 11 84.6 15.4 40.8
83894 58.9 173.1 19.7 79.9
83895 56.2 154.5 23.5 85
83896 36.9 133.7 20.6 70.5
83897 79.1 160.6 30.7 100.4
83898 86 185.4 25 97
83899 75.3 177 24 83.2
83900 73 165.9 26.5 102.2
83901 38.5 139 19.9 70.2
83902 90.7 188.5 25.5 96.7
83903 110.2 161.1 42.5 123.8
83905 54.7 139.3 28.2 90.7
83906 44.8 156.3 18.3 68.5
83907 71.5 172.4 24.1 86
83908 70.5 169.1 24.7 88
83909 95.7 159.1 37.8 117.6
83910 73.2 178.9 22.9 81.1
83911 91.1 172.3 30.7 101.6
83912 14
83913 72.5 171.6 24.6 95
83914 99.3 171.5 33.8 115.4
83915 90 173.6 29.9 109
83916 34.7 132.4 19.8 61.5
83917 68.2 156.9 27.7 82
83918 51.6 162.8 19.5 65.5
83919 64.7 172.9 21.6 76.1
83920 85.7 156 35.2 111.7
83921 62.1 159.3 24.5 87
83922 9.5
83923 11
83924 93.8 162.4 35.6 122.4
83925 57.9 154.1 24.4 90.1
83926 77.8 170.5 26.8 93.5
83928 55.4 154 23.4 94.9
83929 55.3 152.7 23.7 77
83930 71.6 176.6 23 78
83931 78.7 174 26 89
83932 65.7 156.3 26.9 94
83933 90.8 164.6 33.5 102.2
83934 49.7 170.2 17.2 64
83935 55.7 154.4 23.4 86.6
83936 56.8 155.5 23.5 90.8
83937 56.4 152.3 24.3 87.9
83938 82.5 173.3 27.5
83939 7.4
83940 58.9 167 21.1 75.3
83941 68.9 166.6 24.8 85.9
83942 7.7
83943 71.3 163.2 26.8 84.4
83944 92.3 173 30.8 104.3
83946 116.7 181.9 35.3 115.8
83947 73.5 168.4 25.9 96.6
83948 48.9 152.9 20.9 72
83949 78.9 160 30.8 110
83950 71.4 172.7 23.9 89.2
83951 56.5 164.1 21 70.3
83952 74.3 161.2 28.6 97.1
83953 67.9 153.8 28.7 93
83954 78.4 174.1 25.9 94.6
83955 93.1 176 30.1 103.3
83956 8.3
83957 5.1
83958 58.6 160.6 22.7 77.9
83959 126.3 162.9 47.6 129.7
83960 47.4 151.3 20.7 70.4
83961 73.2 154.7 30.6 97.5
83962 68.4 166.5 24.7 88
83963 147 167.9 52.1
83964 67 149.4 30 94
83965 129.3 179.4 40.2 134.9
83966 120.1 180 37.1 114.6
83967 60.9 169 21.3 77
83968 37.2 142.1 18.4
83969 95.8 164.9 35.2 107.2
83970 25.1 124.8 16.1 54.9
83971 109.2 167.5 38.9 112.4
83972 49.1 142.6 24.1 87
83973 93.1 178.1 29.4 103.1
83974 13.5
83975 77.6 155.3 32.2 101.5
83976 74.6 169.5 26 98.9
83977 48.2 152.1 20.8 78.1
83978 32.8 132.9 18.6 57.9
83979 101.2 177.2 32.2 99.6
83980 57.7 142.1 28.6 83.2
83981 57.8 167 20.7 72.1
83982 71.4 176.2 23 78.8
83984 23.9 123.2 15.7 57.2
83985 57.5 176.5 18.5 69.5
83986 98.1 180.9 30 108
83987 97.1 178.4 30.5 113.4
83988 105.1 178.4 33 111.2
83989 72.2 159.3 28.5
83990 66.8 151.4 29.1 105.8
83991 84.6 166.7 30.4 98
83992 61.5 164.9 22.6
83993 121.9 156.4 49.8 141
83994 96.8 176.2 31.2 108.1
83995 143.6 182.4 43.2 136.6
83996 91.3 166 33.1 112.5
83997 75.3 160.8 29.1 102.5
83998 48.6 157.3 19.6 67.1
83999 73.4 171.5 25 89.9
84000
84001 78 168.5 27.5 94
84002 98.1 175.1 32 110.6
84003 14.4
84004 101.7 160.5 39.5 118
84005 137.7 173.6 45.7 128.2
84006 85 159.8 33.3 104
84008 60.1 153.9 25.4 86.7
84009 33.9 132.5 19.3
84010 55.4 160.8 21.4 82.5
84011 119.6 178.2 37.7 129.3
84012 69.2 177.6 21.9 83.6
84013 59 173.4 19.6 75.5
84014 70.4 167.5 25.1 87.3
84015 71.6 161.4 27.5 106.5
84016 68.9 169 24.1 88.4
84017 27.1 128.6 16.4 62.2
84018 110.1 192.9 29.6 105.4
84019 82.2 169.7 28.5 93.6
84021 81.5 162.5 30.9 105.6
84022 158.2 164.1 58.7 164
84023 49.4 156.2 20.2 71.7
84024 17.1 105.9 15.2 51.8
84025 96.2 168.2 34 92.7
84026 136.2 174.6 44.7 142
84027 14.4 91 17.4
84028 60.3 161.3 23.2 86.6
84029 51.1 158.5 20.3 77.4
84030 63.8 159.3 25.1 91.6
84032 78.4 171.1 26.8 98.5
84033 89.7 163.4 33.6 96
84034 44.6 150.8 19.6 68.8
84035 46.4 147.3 21.4 76
84036 100.2 186.5 28.8 110.5
84037 78.8 178.3 24.8 93.5
84038 82.8 161.2 31.9 101.4
84039 73.4 161.2 28.2 95.9
84041 60.8 161.1 23.4 89.4
84042 63.9 181.8 19.3 85.2
84043 4.4
84045 36.4 139.3 18.8
84046 90.4 165 33.2 114.5
84047 50.7 151.6 22.1 81.2
84048 4.9
84049 120.4 167.4 43 131
84050 70.5 157.1 28.6 101.4
84051 95.9 171.9 32.5 105.9
84052 29.7 132.5 16.9 57
84053 12
84054 92.4 171.9 31.3 99.5
84055 49.5 154.3 20.8 82.2
84056 63.4 148.9 28.6 84.7
84057 12.9 93.2 14.9 44
84058 63.2 165.4 23.1 78.3
84059 14.9 103.2 14 45.3
84060 9.1
84061 68 158 27.2 98.5
84062 80.4 154.1 33.9 107.6
84063 44.8 160 17.5 67.2
84064 7.3
84065 67.4 161.4 25.9 89.6
84066 56.6 174 18.7 75.7
84067 4.2
84068 80.6 172.6 27.1 96.5
84069 83.8 168.2 29.6 104.5
84070 91.2 176.2 29.4 105.3
84072 86.9 164 32.3 99.5
84073 80.2 158.5 31.9 103.1
84074 59.8 146.1 28 95
84075 178.9
84077 76.4 157.4 30.8 105.3
84078 32.4 133.2 18.3 61.2
84079 52.8 154.3 22.2 74.1
84080 17.2
84081 8
84082 51.8 158.4 20.6 74.4
84083 13.3
84085 27.5 128.6 16.6 55.2
84086 84.9 174.5 27.9 96.1
84087 60.7 164 22.6 76.5
84088 60 161 23.1 84.3
84089 78.2 183.3 23.3 95.8
84090 89.1 167.7 31.7 98.6
84091 60.6 162.7 22.9 74.4
84092 51.3 148.7 23.2
84093 71.7 163.8 26.7 82
84094 57.3 159.4 22.6 83.4
84095 69.8 160 27.3 96.1
84096 30.8 137.7 16.2 55.1
84097 20.5 115.2 15.4 49.7
84098 67.3 177.4 21.4 73.8
84099 91.3 169 32 116.9
84100 77.7 164.2 28.8 98
84101 108.3 176.8 34.6 130.7
84102 88.7 162.5 33.6 91.3
84103
84104 10
84105 89 189.4 24.8 96.2
84106 68.5 166.8 24.6 85.9
84107 53.3 149.6 23.8 81.7
84108 186.5 97.5
84109 87.5 179.1 27.3 104.6
84110 74.3 165.8 27 94.4
84111 108.2 173.2 36.1 118.5
84112 69.1 171.4 23.5 86.3
84113 31.7 122.8 21 67.8
84114 63.2 165.1 23.2 96.9
84115 68.7 164.2 25.5 101.7
84116 11
84117 44.5 147.4 20.5 68.8
84118 53.2 150.1 23.6 82.8
84119 73.8 164.6 27.2 98.6
84120 63.4 154.1 26.7 91.6
84121 83.2 176.7 26.6 93.8
84122 107.6 165.2 39.4 127.1
84123 20.3 121.2 13.8 51.1
84124 7.7
84125 73.8 155.9 30.4 106.4
84126 131.6 179 41.1 136.1
84127 44.8 149.9 19.9 71.8
84128 78.7 163.7 29.4 95.5
84129 48.2 154 20.3 77.9
84130 62.5 174.5 20.5 78.3
84131 18.5 110.8 15.1 55
84132 15.4 99.6 15.5 50
84133 19.1 113.1 14.9 55.6
84134 46.7 159.8 18.3 69.4
84135 8.2
84136 33.6 132.5 19.1 68.3
84137 50.8 161.6 19.5 72.7
84138 13.5
84139 45.9 153.7 19.4 84.1
84140 64.9 166.2 23.5 74.6
84141 44.8 142.2 22.2 80
84142 102.3 176.7 32.8 113.3
84143 73.4 159.3 28.9 100
84145 18.1 100.6 17.9 56
84146
84147
84148 10.6
84149 35.6 138.7 18.5 68.7
84150 14.6 95.6 16

Statistics homework help

Create a prototype of a dashboard that displays the following Key Performance Indicators for a hospital, it should include:

· Average treatment costs for patients by age groups in the following age groups: 0–1, 2–17, 18–44, 45–64, 65–84, 85+

· Number of monthly hospital admissions

· Number of monthly hospital readmissions

· Distribution of the length of stay in the hospital

You can use excel to compile this information. It is more important to focus on which chart would best display the information and how the information should be displayed.

120 POINTS

Statistics homework help

EXAMPLE1.pdf

Data Report #1

A History of the
American Economy

Tiffany Diep

Professor Surro

ECON 165

4 February 2022

Introduction

This data report aims to provide statistical and economic insight towards the historical

development of the United States from 1870 to 2017.

● The country has seen immense growth since its establishment in the late 18th century,
transforming from a series of British colonies into one of the most powerful independent

economies in the world.

● The American government and people have experienced periods of regulation,
revolution, democratization, capitalism, industrialization, wars, recessions, and booms in

order to form itself into the global business powerhouse that it is today.

● To summarize it concisely, the years between 1870 and 2017 have been split into six
distinct time periods that will allow for a closer look at key events in American history and

their effects on the data.

Multiple variables will be used to analyze these economic trends, including Real GDP per capita,

Consumer Prices, Government Expenditure, Government Revenue, Short-term Interest Rates, and

House Prices.

Source: Òscar Jordà, Moritz Schularick, and Alan M. Taylor. 2017. “Macrofinancial History and the

New Business Cycle Facts.” in NBER Macroeconomics Annual 2016, volume 31, edited by Martin

Eichenbaum and Jonathan A. Parker. Chicago: University of Chicago Press.

1

1870-1914: Railroads, Steel, Electricity, and Banking

The graph below depicts Real GDP per capita based on purchasing power parity rates (PPP). This

means that the yearly gross domestic product from the United States is converted into

international dollars and divided by the total population in the country. This variable is able to

measure the value of economic production per each individual American citizen.

An increase in Real GDP per capita can be explained by a strengthening economy that has higher

spending and aggregate demand for all goods/services, and a growing workforce which is able

to meet this demand by producing more. This trend can be seen consistently between 1870 and

1914, resulting in a net increase of Real GDP per capita by 2354 units.

A decrease in this variable can be alternatively caused by a reduction in aggregate demand that

leads to declines in revenue and employment. This can result from a lower level of productivity

and a growing population that reduces the amount of economic value attributed to each citizen

when calculating Real GDP per capita. Instances of these downturns can be seen in the graph

most notably in 1894, 1908, and 1914.

Overall, Real GDP per capita increased from 2445 to 4799 over the course of 44 years due to the

focus on improving industry and infrastructure during this period of time.

2

1914-1929: World War I and the Roaring Twenties

The Consumer Price Index (CPI) determines the weighted average of the price for a “basket of

goods.” This basket consists of basic consumer goods and services that can include food,

clothing, shelter, healthcare, education, transportation, and recreation. The change in prices can

be useful in measuring the cost of living over time.

CPI increases when the price of each good in the basket increases. The cost of these products

often rise due to inflation, and this is the case when looking at the trend between 1914 and 1920

where consumer prices doubled from 8 to 16 after World War I.

Similarly, the variable decreases whenever prices decrease from deflation. Additionally,

consumers may choose to find substitutes for their purchases in response to price changes, and

this can also lower the CPI because it alters the weight of each good in the basket. The chart

above shows a decrease from the spike in 1920 and prices begin to correct a year later, staying

constant at 14 throughout the rest of the Roaring Twenties.

This trend of inflation and deflation affecting the CPI is commonly seen during periods of war. The

inflation is caused by a shortage of resources or pent-up demand during the wartime effort, and

deflation begins to kick in after the government removes their control on the economy following

the aftermath.

3

1929-1945: The Great Depression and World War II

Government Expenditure includes the purchase of goods and services by federal, state, and local

governments for public consumption or investment. Government spending is funded mainly by

tax collection and income from public sectors like railroads.

An increase or decrease in Government Expenditure first takes into consideration the size of the

current budget deficit and the amount of national debt withstanding. If there is a large deficit and

a lot of debt, the government may be less likely to spend. However, spending can have the

potential to efficiently stimulate the economy in a way that leads to a boost in growth and GDP.

In the graph above, Government Expenditure during The Great Depression from 1929 to 1933

remained quite low. During World War II, there was a huge increase in government spending that

jumped from $9 billion in 1939 to $93 billion in 1945, making it the most expensive war in

American history. A majority of this spending went towards reforming factories and mass

producing resources and equipment for the wartime effort. As a result, many more jobs were

created and the unemployment rate declined significantly, marking this time as the beginning of

an economic boom.

4

1945-1973: Post-World War II Prosperity

Government Revenue is mainly collected through tariffs, consumption tax, and income tax. This

revenue is typically used to finance goods and services for American citizens and businesses.

The government’s main method of generating more revenue is by increasing tax rates or

reducing the amount of tax breaks. The trend in the graph shown above demonstrates consistent

upward movement, increasing from $45 billion in 1945 to $231 billion 1973. This can be explained

by the high tax rates after World War II that reached a high of 94% in certain years. During a time

of economic boom and prosperity, tax revenues often increase.

5

1973-2000: Inflation and Globalization

The Short-term Interest Rate is essentially the cost of borrowing money, and it is determined

through the market factors of supply and demand for monetary funds. Based on three-month

money market rates, it includes the average of daily rates shown as a percentage per year.

A number of factors can affect the determination of interest rates, including fiscal policy,

monetary policy, and inflation. Expansionary fiscal policy and contractionary monetary policy can

increase interest rates, while contractionary fiscal policy and expansionary monetary policy can

decrease interest rates. Higher interest rates are often helpful in reducing the amount of inflation

in the economy.

In the line chart above, the Short-term Interest Rate reached an extreme high of 16% in 1981,

compared to 9% at the beginning of the time period in 1973 and an even lower 6% at the end of

the time period in 2000. This may be due to the recessions and the resulting high levels of

inflation during the early 1980s. Strict government policies were most likely implemented in an

attempt to raise interest rates and bring inflation back down to a normal level.

6

2000-2017: The Housing Crisis and Aftermath

The House Price Index (HPI) aims to measure the change in price of single-family homes in the

United States. The prices are measured as a percentage change from the base year, which is

1990 in this case, and so the HPI at that time would be 100.

House prices function similarly to other goods and services in the free market, so when demand

goes up and supply goes down, houses get more expensive. Alternatively, when demand

decreases and supply increases, houses become more affordable.

In the case of the 2008 housing crisis, the HPI reached an additional 75% increase in house

prices after the initial 42% change in 2000. As demand remained high and the housing supply

stayed relatively stagnant in recent years, the house prices continued to steadily increase. In

2017, the HPI grew to its highest at 255, resulting in a net increase in house prices of 113%

compared to the beginning of the time period and it may be expected to continue growing.

7

Conclusion

Between the years of 1870 and 2017, the United States has gone through periods of both growth

and struggle. It is clear to see how the history of politics and economics are extremely intertwined

in a way that one thing affects the other.

● By looking at key events during the six time periods including the development of
American capitalism, both World Wars, the Roaring Twenties, the Great Depression, and

the Housing Crisis of 2008, it is useful to associate these turning points in U.S. history

with relevant variables that can help explain why the economy responded the way that it

did.

The analysis of Real GDP per capita, Consumer Prices, Government Expenditure, Government

Revenue, Short-term Interest Rates, and House Prices throughout the data report help to

describe the functions of different economic measurements and how they can be used to provide

more background for historical trends in the U.S.

8

EXAMPLE2.pdf

Econ 165 Data Report 1

Christopher Surro

Table of Contents ◉ Introduction

◉ Period 1: 1870-1920

◉ Period 2: 1920-1970

◉ Period 3: 1970-2017

◉ Conclusion

Introduction

Introduction
This report has been put together in order to provide a clear and concise overview of the history of the U.S. Economy. A total
of 12 variables have been pulled from a data source, categorized, transformed, and separated into three time periods of
approximately 50 years each. The variables have been organized under five of the most indicative categories of the U.S.
economy: Nation, Government, Consumption, Banks, and Housing. There is also a short section dedicated to Financial Crises,
which is only included to add to the picture of the U.S. economy. By organizing the raw data into these five categories, it is
hoped that an understanding of the history of the U.S. economy will be more accessible.

It is important to note that many of the variables have been converted from nominal values into real values by dividing the
original nominal data by the CPI, which has a baseline year of 1990. In addition, there are several instances in which variables
were computed as a percentage of GDP by dividing the original nominal data by the nominal GDP.

Variables: Current Account, Imports, Exports, Government Revenue, Government Expenditure, Government Revenue &
Expenditure as a Percent of GDP, Consumption Per Capita, GDP Per Capita, Consumption Per Capita as a Percent of GDP Per
Capita, Bank Capital Ratio, Loan to Deposit Ratio, Home Prices, Mortgage Loans to Non-Financial Private Sector, and Financial
Crises.

Time Periods: 1870-1920, 1920-1970, 1970-2017.

All variables will be graphed over time, and some will be graphed together in order to provide a holistic picture of a certain
economic sector.

Period 1: 1870-1920

Nation

Current Account: There is no movement in the U.S.
current account until right before 1915, when there is a
sharp increase from $0 to about $0.35 billion. From
1915-1920 the current account is unsteady and seems
to be declining at the end of this 50 year period. It is
interesting to note that although there is movement in
imports and exports (which are included in a
country’s current account) before 1915, the current
account itself remains at $0.

Imports: After some instability from 1870-1880,
imports remain steady around $0.125 billion until
1905. After that, imports increase from $0.125 billion in
1905 to $0.3 billion in 1920. This is almost a 150%
increase in only 15 years.

Exports: After an increase between 1870-1875, exports
remain stagnant around $0.125 billion until 1900. After
1900, instability returns. Overall, exports increase
substantially in the last 20 years of this period, starting
at $0.125 billion in 1900 and ending at $0.5 billion in
1920. This is a 300% increase.

Government

Government Revenue: There is no movement in government revenues until the 5 years between 1895-1900. At this point, revenues
increase from $0 to $0.15 billion and remain like this until the 5 years between 1915-1920. At this point, revenues increase quite
substantially and at the end of this 50 year period, they are almost at $0.5 billion.
Government Expenditure: Similarly to government revenue, expenditure does not move from $0 until the 5 years between 1895-1900.
At this point, expenditures increase from $0 to $0.15 billion. After a dip back to $0 in 1902, expenditure begins increasing significantly
from 1915-1920. During the last 5 years of this time period, expenditures increase by 200%.
Government Revenue and Expenditure as a Percent of GDP: Both variables have very similar movement to government revenues and
expenditures. It is only important to note that the most movement occurs from 1915-1920. Expenditures make up almost 23% of GDP in
1920, while revenues make up almost 8% of GDP.

Consumption

Consumption Per Capita: Despite some instability in consumption per capita during the first 50 years, there is an overall increase. In
1870, consumption per capita is at an index level of 8, indicating that it is 92% lower than the 2006 base year. This is reasonable given
the large time difference. In 1920, consumption per capita is at an index level of 16, indicating that it is 84% lower than the 2006 base
year.
GDP Per Capita: GDP PC mirrors consumption PC pretty similarly for the first 50 years, with GDP PC consistently remaining below
consumption PC. There is a steady increase in both variables from 1870-1920, with a slight decrease towards 1920.
Consumption Per Capita as Percent of GDP Per Capita: Consumption PC remains, on average, unchanged. In this first 50 year period it
makes up about 130% of GDP PC.

Banks

Bank Capital Ratio: The capital ratio of banks starts at
about 32% in 1870. This is a high ratio and indicates
that U.S. banks were at a position to handle losses
well. By the 1920s, however, the ratio is right under
10%. This 20% decrease signals that U.S. banks were
potentially taking on more risk and would not be
positioned to handle any downturns as well as they
would have been at the start of this period.

Bank Loan to Deposit Ratio: The loan to deposit ratio
starts at 120%, indicating that for every bank deposit
there were 1.2 bank loans. This is not great because it
means that banks are loaning away more money than
they actually have, stripping them of liquidity. Almost
immediately, the ratio drops down to below 100%. By
1920, this ratio decreased to about 85%. This could
mean that there were more bank deposits or less bank
loans at the end of this period. Either way, the drop in
percent is a good sign because it indicates higher bank
liquidity.

Housing

Home Prices: There is no data available on home prices until 1890. The index level on home prices remains constant at about 0.42 until a
sharp increase occurs in 1900. After this, the home price index is inconsistent, with sharp increases and decreases. In 1920, home prices
are indexed at 0.44, which is only .02 higher than in 1890. There is very little growth in home prices during these 30 years.

Mortgage Loans to Non-Financial Private Sector: There is no data available for this variable until 1880. Overall, there seems to be a step
pattern in this graph, as loans sharply increase and then remain stagnant for a few years repeatedly. From 1880-1890, mortgage loans
were at about $0.125 billion. By the end of this period, mortgage loans were worth $0.5 billion. This is a 300% increase in mortgage loans
to the non-financial private sector (which includes households) in the span of 40 years. Although there were some points of decrease,
overall the mortgage loan market grew dramatically during this period. This can indicate a few things: more people were buying property,
more people could not afford property, or banks were more lenient with lending.

Financial Crises

During the 50 year time period from 1870-1920, there
were three financial crises. They occured in 1873, 1893,
and 1907.

Period 2: 1920-1970

Nation

Current Account: Although the U.S. current account still
averages at around $0-0.1 billion, there is more volatility
during these middle 50 years. This makes sense
because the economy is growing and progressing as
time moves forward. Between 1945-1950 (post WWII),
there is a sharp increase to $0.5 billion followed by a
drop back down to $0. It remains interesting to note
that although there is clear growth in imports and
exports (which are included in a country’s current
account), the current account itself grows very little.
Imports: There is a clear upwards trend in imports
during this period. Imports start at $0.3125 in 1920, and
grow to over $1.8 billion by 1970. This increase of almost
$1.5 billion indicates a growth in globalization and trade.
Exports: Similarly to imports, there is a clear growth in
exports. Exports start at $0.5 billion in 1920, and grow
to over $1.9 billion by 1970. Again, this increase of
approximately $1.4 billion not only indicates a growth in
globalization, but it also indicates that the U.S. is keeping
up with the expansion of the global economy. The
sharpest growth in exports occurs from 1940-1945, the
years of World War II, which indicates that the U.S. was
exporting many war-related goods.

Government

Government Revenue: Although government revenues slightly increase from 1920-1940, the largest jump occurs between 1940-1945. In
fact, revenues grow by over 370% during these five years. This growth in revenue can mostly be attributed to World War II and
European expenditure on American war goods. After 1945, revenues suffered a slight decrease of 30%, followed by consistent growth
of about $1 billion every five years. This is a sign of a progressing and strengthening economy.
Government Expenditure: Expenditures follow a similar path as revenues during this middle 50 year period, only on a slightly larger
scale. Again, the predominant growth of expenditures occurs from 1940-1945, presumably due to World War II. Expenditures grew by
over 650% during the years of the war. After 1945, expenditure dropped by over 60%, followed by consistent growth.
Government Revenue and Expenditure as a Percent of GDP: Both variables have very similar movement to government revenues and
expenditures. Both revenues and expenditures make up a much higher percentage of GDP during the years of World War II. Although
these percentages decrease post-war, they are still over 10% greater than pre-war.

Consumption

Consumption Per Capita: Unlike the previous period, consumption PC follows a steady path of increase from 1920-1970. There is no
notable growth during the years of World War II. The only important thing to note is that consumption PC grew from an index level of
16 to an index level of 44.
GDP Per Capita: GDP PC also follows a steady path of growth during this period. There is a notable increase in GDP PC from
1940-1945, the years of World War II. GDP PC grows from an index level of 21 to an index level of 34, and continues to grow postwar
despite a slight dip.
Consumption Per Capita as Percent of GDP Per Capita: Interestingly, consumption PC makes up less of GDP PC at the end of this
period than it did at the end of the last period. During the years of World War II, consumption PC drops from 100% to about 67%. This
drop may potentially be due to war-related factors making up a higher percentage of GDP PC.

Banks

Bank Capital Ratio: The capital ratio of banks starts at
almost 8% in 1920. This ratio progressively decreases
during this period, albeit on a small scale. The most
noticeable dip occurs from 1940-1945. By 1970, the
bank capital ratio is at just over 5%. This is quite low
compared to the preceding 50 years, and may
indicate that banks lost liquidity.

Bank Loan to Deposit Ratio: The loan to deposit ratio
starts at about 85%, indicating that for every bank
deposit there were 0.85 bank loans. This ratio drops
significantly (almost 80%) from 1930-1945, which may
be related to the Great Depression and World War II.
The extremely low loan to deposit ratio by 1945
indicates that banks were much more liquid. After
1945, the ratio consistently increases, until it reaches
60% in 1970. Overall, the loan to deposit ratio was cut
in half from 1870-1970.

Housing

Home Prices: The index level on home prices remains stable at about 0.6 until a sharp increase occurs postwar. This increase boosts
home price index levels to about 0.9, which is extremely close to 1990 base year prices. It is interesting to note the dip in home prices
during the early years of World War II and their quick recovery in the late years of World War II and postwar.
Mortgage Loans to Non-Financial Private Sector: Mortgage loans experience a dramatic total increase during this 50 year time period.
Post World War II, mortgage loans significantly increase and continue to do so until 1970. Mortgage loans grow from $0.5 billion to
over $9 billion from 1920-1970, which is a 1,700% increase. This is huge and can partially be attributed to the increase in home prices
that occurred postwar. There may also be a connection between Loan to Deposit ratios dropping in other loan categories (as
discussed in the previous slide), allowing banks to allocate more money to mortgage loans.

Financial Crises

During the 50 year time period from 1920-1970, there
was one financial crisis. This crisis occurred in 1930.

Period 3: 1970-2017

Nation

Current Account: There is a slight decrease in the U.S.
current account from 1970-2017. Although the U.S.
current account still averages at around $0 until 1992,
it begins to drop below $0 after that. In 2017, the
current account actually hovers around -$2.4 billion. It
remains interesting to note that although there is clear
growth in imports and exports (which are included in
a country’s current account), the current actually
decreases.
Imports: There is a clear upwards trend in imports
during this period. Imports start at $1.8 in 1970, and
grow to over $16 billion by 2017. This increase of
almost 790% indicates a very large growth in
globalization and trade.
Exports: Similarly to imports, there is a clear growth in
exports. Exports start at $1.9 billion in 1970, and grow
to almost $13 billion by 2017. Again, this increase of
approximately 585% not only indicates a growth in
globalization, but it also indicates that the U.S. is
keeping up with the expansion of the global economy.

Government

Government Revenue: Government revenues have their highest and most consistent increase during this 50 year period. Besides for a
large decrease which occurs in 2008, most likely due to the Great Recession, revenues are trending upwards. In 1970, revenues are at
$6.2 billion and by 2017, they grow to $18.2 billion.
Government Expenditure: Expenditures follow a similar path as revenues during this 50 year period, only on a slightly larger scale.
Again, the growth is very consistent, despite the Great Recession. In fact, government expenditures actually increase by almost 25%
from 2007-2009. This makes sense because of the government’s deficit spending during those few years. In 1970, revenues are at $6.3
billion and by 2017, they grow to $21.8 billion.
Government Revenue and Expenditure as a Percent of GDP: Both variables almost follow an opposite path during this period. Similarly
to what was stated above, although revenues make up less of GDP during the Great Recession, expenditures make up more of it.

Consumption

Consumption Per Capita: Consumption PC continues to follow a steady path of increase during this period. There is a very small dip in
consumption PC during the Great Recession, but it is barely noticeable. It is important to note that consumption PC grew from an
index level of 44 in 1970 to 111 in 2017, which is a growth of over 150%. This also means that by 2017, consumption PC was 11% than the
base year of 2006.
GDP Per Capita: GDP PC also continues to follow a steady path of growth during this period. It’s growth mimics consumption PC
almost exactly, especially during the Great Recession. GDP PC grows from an index level of 49 to an index level of 110, which is a
growth of almost 125%. This also means that by 2017, GDP PC was 10% than the base year of 2005.
Consumption Per Capita as Percent of GDP Per Capita: Consumption PC continuously makes up more and more of GDP PC during this
period. By 2017, consumption PC essentially makes up 100% of GDP PC.

Banks

Bank Capital Ratio: The capital ratio of banks starts at
5.27% in 1970. This ratio progressively increases
during this period, albeit on small scale. By 2017, the
bank capital ratio is at just over 9%. This is higher than
the end of the preceding 50 years, and may indicate
that banks gained liquidity.

Bank Loan to Deposit Ratio: The loan to deposit ratio
starts at about 60%, indicating that for every bank
deposit there were 0.6 bank loans. This ratio
decreases significantly (almost 17%) from 2007-2010,
and continues to decrease until 2013. It makes sense
that this ratio would drop during the years of the Great
Recession because of the housing market crash. It is
also interesting to point out the increase in the loan to
deposit ratio in the years preceding the Great
Recession, otherwise known as the Housing Bubble.
In 2017, the ratio is just over 71%. Overall, the loan to
deposit ratio grew by about 18% from 1970-2017.

Housing

Home Prices: The index level on home prices remains stable until 2000, when it begins to increase quite dramatically. From
1995-2005, the home price index grows by 0.5. However, from 2006-2013, the price index decreases at the same rate that it
increased. Again, this increase and decrease is most likely due to the housing bubble followed by the Great Recession. Overall, the
home price index grows from 0.9 to 1.4 during this time period.
Mortgage Loans to Non-Financial Private Sector: Mortgage loans experience a large increase during this 50 year time period. Despite
a slight decrease during the Great Recession years, mortgage loans grow by 355% from 1970-2017. Although this growth is much
smaller than the preceding 50 years, it is still large.

Financial Crises

During the 47 year time period from 1970-2017, there
were two financial crises. They occured in 1984 and
2007.

Conclusion

Conclusion
There has been a lot of information to cover in ensuring that a cohesive picture of U.S. economic history is presented. Although all five sectors have
had continuous overall growth during the 147 years discussed, it is needless to say that the country suffered numerous periods of downturn. Most of
these occurred during the same years as the financial crises, such as the Great Recession. Periods of growth can also be clearly attributed to
historical events, such as World War II. Overall, it can be seen that in every sector, the U.S. economy pushes through struggles and crises in order to
pursue continuous growth.

The first time period of 1870-1920 can be characterized by little to no growth, followed by sudden volatility. Although some variables experienced a
lot of upturns and downturns in the last 20 years of this time period, because of the lack of movement in the first 30 years, it can still be interpreted
as growth for the U.S. economy. Given the fact that the U.S. was still a young country in the 1800s, it is not surprising that there was not much
movement in many variables, most notably government revenues and expenditures, until the 1900s.

The second time period of 1920-1970 can be characterized by consistent growth, despite high volatility. The Great Depression seemed to have the
largest effect on Banks’ Loan to Deposit Ratio. However, despite this financial crisis, the U.S. economy increased greatly during these 50 years. Some
of this can be attributed to World War II, which spurred a lot of international trade and purchases, as can be seen by the increase in exports from
1940-1945. Overall, the U.S. seems to be heading towards a bright economic future at the end of these 50 years.

The third time period of 1970-2017 can be characterized by a continuation of growth, albeit at a less dramatic rate. Although almost all variables more
or less increase during these 50 years, the percentage of growth is smaller than the preceding 50 years. There are some clear downturns in home
prices, government revenues, and loan to deposit ratios during the years of the Great Recession, which makes sense. In addition, it is interesting to
see the sharp increase in government expenditure during the Great Recession. Overall, these last 50 years indicate steady economic growth.

It is promising to see that despite numerous financial crises, recessions, depressions, and wars, the U.S. economy has the ability to push through
them. These 147 years included a lot of challenging times for the U.S., but the strength and growth of the U.S. economy is undeniable.

EXAMPLE3.pdf

Econ 165: Data Report 1

Robert Priolo

February 4, 2022

1 Overview

The following data report will review the economic history of the United States over the past 147 years.
This report will examine historical trends of economic data in America, including population, GDP, CPI
and inflation data, long-term and short-term interest rates, and finally, mortgage spending. Key statistical
data is provided for each metric showing their means throughout the history of the United States, along
with percentage changes from year to year. This report will also examine the correlations between GDP,
CP

Statistics homework help

Instructions – Read First

Respondent sequence number Gender Age in years at screening Race/Hispanic origin Education level – Adults 20+ Marital status Annual family income Ratio of family income to poverty
83732 1 62 3 5 1 10 4.39
83733 1 53 3 3 3 4 1.32
83734 1 78 3 3 1 5 1.51
83735 2 56 3 5 6 10 5
83736 2 42 4 4 3 7 1.23
83737 2 72 1 2 4 14 2.82
83738 2 11 1 6 1.18
83739 1 4 3 15 4.22
83740 1 1 2 77
83741 1 22 4 4 5 7 2.08
83742 2 32 1 4 1 6 1.03
83743 1 18 5 15 5
83744 1 56 4 3 3 3 1.19
83745 2 15 3 4 0.86
83746 2 4 5 12
83747 1 46 3 5 6 3 0.75
83748 1 3 4 6 0.94
83749 2 17 3 14 3.16
83750 1 45 5 2 5 4 1.36
83751 2 16 1 4 0.58
83752 2 30 2 4 6 15 5
83753 1 15 4 8 2.49
83754 2 67 2 5 1 6 0.89
83755 1 67 4 5 2 5 2.04
83756 1 16 3 7 1.11
83757 2 57 2 1 4 5 0.77
83758 1 80 3 5 2 9 4.71
83759 2 19 1 7 1.74
83760 2 3 4 7 1.1
83761 2 24 5 5 5 1 0
83762 2 27 4 4 5 6 2.12
83763 2 2 2 9 1.94
83764 1 14 3 15 5
83765 2 0 3 9 3.17
83766 2 10 3 14 3.34
83767 2 54 5 4 3 14 2.99
83768 2 15 3 6 1.09
83769 1 49 5 2 1 10 2.97
83770 1 15 4 4 0.66
83771 2 2 1
83772 2 2 5 5 1.25
83773 2 80 3 3 2 7 3.57
83774 2 13 3 15 4.3
83775 2 69 2 1 4 2 0.55
83776 2 58 1 5 1 14 3.72
83777 1 56 5 2 1 7 1.35
83778 1 16 2 5 0.99
83779 2 1 5 99
83780 1 4 1 14 2.82
83781 2 27 4 5 5 77
83782 2 0 3 7 0.98
83783 1 17 3 15 4.28
83784 1 22 2 4 5
83785 2 60 2 5 3 15 5
83786 1 51 4 4 5 77
83787 2 68 1 1 3 4 1.49
83788 2 69 3 4 1 7 1.79
83789 1 66 3 5 6 9 5
83790 1 56 3 1 1 4 1
83791 2 80 3 2 1 12
83792 2 3 1 7 2.51
83793 2 11 3 7 1.23
83794 2 10 4 15 4.23
83795 1 5 3 9 2.3
83796 2 4 3 6 1.32
83797 2 1 2 15 4.22
83798 2 0 5 15 5
83799 2 37 2 4 1 14 4.18
83800 1 10 4 9 2.57
83801 2 80 3 5 1 77
83802 2 29 1 3 1
83803 1 27 4 4 3 6 2.36
83804 1 1 1 4 0.57
83805 2 7 4 7 1.89
83806 2 2 3 1 0
83807 2 10 1 12
83808 1 4 5 10 1.91
83809 2 20 4 3 5 14 3.3
83810 2 6 4 7 1.1
83811 2 7 3 15 4.68
83812 2 68 1 3 1 15 5
83813 1 24 3 4 3 6 2.89
83814 2 11 2 15 4.73
83815 2 15 4 6 0.77
83816 1 27 3 4 6 1 0
83817 1 42 3 5 1 15 4.22
83818 2 80 2 1 2 3 0.84
83819 2 16 3 8 2.07
83820 1 70 3 5 6 8 4.18
83821 1 80 3 1 2 3 1.03
83822 2 20 4 4 5 6 1.62
83823 2 29 1 1 5 3 0.35
83824 1 23 5 5 5 1 0
83825 2 16 4 6 0.77
83826 1 6 1 77
83827 1 61 4 3 1 10 4.39
83828 2 39 1 3 1 4 0.49
83829 1 50 5 5 1 15 5
83830 1 15 4 8 1.98
83831 2 15 5 6 0.6
83832 2 50 1 1 4 7 1.41
83833 1 14 3 10 2.98
83834 1 69 4 3 5 3 0.97
83835 2 13 4 2 0.31
83836 2 18 1 14 2.76
83837 2 45 1 2 1 14 2.18
83838 2 8 1 2 0.17
83839 1 13 3 15 4.32
83840 2 0 1 4 0.75
83841 1 13 5 15 4.12
83842 1 1 3 14 4.46
83843 1 80 3 4 1 8 2.82
83844 1 27 1 2 6 7 1.41
83845 2 44 4 1 5 9 1.5
83846 2 41 4 4 3
83847 1 18 3 15 5
83848 1 10 3 7 1.65
83849 1 71 2 4 1 6 1.34
83850 1 13 3 15 5
83851 2 37 3 3 1 8 1.86
83852 2 0 3 15 5
83853 2 49 3 3 1 15 5
83854 2 46 1 5 1 9 2.39
83855 2 12 3 7 1.65
83856 1 30 3 4 1 8 1.9
83857 2 31 3 5 1 15 5
83858 1 0 1 99
83859 1 2 3 3 0.34
83860 1 41 4 4 1 15 5
83861 1 80 3 5 3 8 4.21
83862 2 19 2 99
83863 1 35 1 3 1 14 2.64
83864 1 4 4 1 0.19
83865 2 21 3 2 5 8 2.14
83866 1 40 4 4 5 14 4.36
83867 1 13 5 7 1.65
83868 2 11 1 15 4.54
83869 2 67 3 5 3 4 1.35
83870 1 48 1 3 1 9 2.24
83871 2 30 1 1 6 6 0.87
83872 1 63 1 3 2 99
83873 1 4 3 15 4.68
83874 1 54 1 2 1 5 1.14
83875 2 42 4 5 1 10 1.82
83876 2 71 3 3 3 2 0.81
83877 2 13 5 14 3.55
83878 1 10 4 13
83879 2 14 3 15 3.87
83880 2 79 3 1 1 3 0.43
83881 2 32 3 5 1 8 2.06
83882 2 4 3 4 0.97
83883 2 80 1 2 5 2 0.68
83884 1 61 1 3 1 4 0.62
83885 2 38 5 4 1 14 3.62
83886 1 74 3 5 1 6 2
83887 2 51 4 2 1 99
83888 1 3 3 10 1.85
83889 1 26 3 5 6 8 4.25
83890 2 18 5 6 0.95
83891 2 54 3 4 5 9 5
83892 2 2 5 4 0.62
83893 2 68 1 1 1 4 1.12
83894 1 60 4 3 1 8 1.23
83895 2 80 3 3 2 4 0.77
83896 2 9 2 5 0.77
83897 2 29 3 5 6 5 1.68
83898 1 55 3 4 1 8 2.68
83899 1 27 3 1 1 6 1.57
83900 2 52 3 5 3 3 0.85
83901 2 10 4 4 0.66
83902 1 49 3 4 1 15 5
83903 2 47 4 4 1 7 2.08
83904 2 80 4 2 1 3 0.75
83905 1 9 2 9 1.47
83906 2 11 5 1 0.01
83907 1 22 5 5 5 2 0.42
83908 1 51 4 3 1 4 1.43
83909 2 49 3 4 1 77
83910 1 37 3 3 6 10 4.37
83911 2 43 4 4 6 14 3.3
83912 1 1 1 7 1.23
83913 1 43 5 1 1 7 1.44
83914 2 23 2 4 5 7 2.32
83915 1 71 1 4 6 6 1.69
83916 2 8 4 14 2.92
83917 2 17 3 5 0.82
83918 1 15 4 14 2.45
83919 1 19 1 6 1.64
83920 2 68 1 1 1 3 0.35
83921 2 10 4 14 2.46
83922 1 1 3 4 0.66
83923 2 1 3 8 1.86
83924 2 48 3 1 1 7 2.5
83925 2 74 2 3 2 8 3.82
83926 1 66 3 4 1 9 3.43
83927 2 66 5 5 1 10 4.06
83928 2 62 1 3 1
83929 2 10 4 2 0.24
83930 1 17 3 5 1.1
83931 1 37 2 2 4 7 2.08
83932 2 80 3 4 1 8 3.14
83933 2 31 3 2 6 7 1.32
83934 2 27 4 3 5 3 0.86
83935 2 44 5 5 1 8 1.86
83936 1 12 3 15 5
83937 2 75 5 1 2 8 1.76
83938 1 45 5 5 1 14 3.55
83939 2 0 3 14 2.99
83940 1 16 2 2 0.28
83941 1 71 2 3 1
83942 1 0 3 15 5
83943 2 17 1 4 0.49
83944 1 75 4 4 6 4 0.74
83945 2 9 1 10 2.46
83946 1 43 3 5 1 15 5
83947 2 33 3 4 1 10 2.67
83948 2 13 1 6 0.8
83949 2 78 3 3 2 6 2.38
83950 1 55 3 2 3 2 0.61
83951 1 24 4 2 5 9 2.98
83952 2 14 1 7 1.23
83953 2 46 1 5 1 15 5
83954 1 53 3 3 1 14 5
83955 1 47 4 4 1 14 4.48
83956 2 0 3 15 4.12
83957 2 0 1 3 0.49
83958 2 47 4 3 3 1 0.25
83959 2 22 3 4 5 4 0.8
83960 1 12 3 15 3.52
83961 2 44 3 4 1 14 3.7
83962 2 28 4 5 5 7 1.65
83963 2 44 4 4 3 6 1.51
83964 2 72 5 2 1 10 4.06
83965 1 49 1 4 3 3 1.24
83966 1 27 1 2 5 4 0.57
83967 1 40 5 5 1 15 5
83968 1 11 3 77
83969 2 21 3 4 1 6 2.01
83970 1 9 5 4 0.95
83971 2 26 3 4 1 9 2.27
83972 2 10 1 8 2.06
83973 1 63 3 5 1 15 5
83974 2 2 5 7 1.17
83975 2 65 2 3 1 14 4.11
83976 1 80 3 4 2 5 2.02
83977 2 80 3 3 1 7 2.5
83978 2 8 4 3 0.6
83979 1 15 1 15 4.44
83980 2 10 3 15 3.52
83981 1 15 4 10 2.67
83982 1 25 3 5 5 15 3.07
83983 2 71 2 5 1 8 2.82
83984 2 6 1 15 5
83985 1 55 3 5 3 15 5
83986 1 40 3 4 1 7 1.11
83987 1 68 1 1 1 3 0.35
83988 1 21 1 3 5 8 1.76
83989 2 37 4 2 5 1 0.16
83990 2 79 1 1 1 3 0.65
83991 2 14 5 6 1.44
83992 1 68 5 5 1 15 5
83993 2 41 4 3 6 6 2.1
83994 2 60 3 5 1 15 5
83995 1 43 4 4 6 9 5
83996 2 60 4 5 2 77
83997 1 13 4 9 1.87
83998 2 31 3 5 5 7 3.57
83999 1 71 5 1 1 3 0.75
84000 1 2 4 1 0.02
84001 2 54 2 4 3 9 4.89
84002 1 48 3 4 3 15 5
84003 2 1 1 99
84004 2 14 1 10 2.68
84005 1 26 4 5 6 5 1.85
84006 2 45 4 2 6 4 0.87
84007 2 27 5 3 5 10 3.42
84008 2 62 5 3 1 7 2.26
84009 2 9 4 15 4.22
84010 2 68 3 3 1 8 3.26
84011 1 32 3 4 1 7 1.43
84012 1 24 1 3 1 10 2.39
84013 1 14 3 8 1.42
84014 1 53 5 5 3 15 5
84015 1 73 1 1 4
84016 2 41 1 5 1 15 5
84017 2 7 2
84018 1 27 3 5 5 10 5
84019 1 54 4 3 1 15 3.55
84020 1 2 3 15 4.96
84021 2 29 5 4 1 8 1.47
84022 2 60 1 4 1 9 2.88
84023 2 19 3 99
84024 1 4 3 15 4.12
84025 2 18 3 8 1.23
84026 1 44 5 4 6 2 0.35
84027 1 2 5 1 0
84028 2 61 3 5 1 15 5
84029 2 28 1 3 1
84030 1 46 1 1 1 77
84031 2 2 5
84032 1 51 1 4 4 77
84033 2 41 5 4 3 9 3.11
84034 2 25 4 4 6 7 1.55
84035 1 10 2 1 0.12
84036 1 36 3 5 1 8 3.37

Instructions: The following worksheets describe two problems – the first problem is for independent samples and the second problem is for dependent samples. Your job is to demonstrate the solution to each scenario by showing how to work through each problem in detail. You are expected to explain all of the steps in your own words.

Independent Samples

Low Lead Level High Lead Level
n1 79 n2 26
93.78 86.9
s1 17.34 s2 9.79
Critical Value:
Test Statistic:
p-value:

1. Write the hypotheses in symbolic form, determine if the test is right-tailed, left-tailed, or two tailed and explain why.

2. Calculate the critical value, the test statistic, and p-value. Show calculations below.

3. Make a decision about the null hypothesis and explain your reasoning, then make a conclusion about the claim in nontechnical terms.

Independent Samples

A researcher conducted a test to learn the effect of lead levels in human bodies. He collected the IQ scores for a random sample of subjects with low lead levels in their blood and another random sample of subjects with high lead levels in their blood. The summary of finding is listed below. Use a 0.05 significance level to test the claim that the mean IQ score of people with low lead levels is higher than the mean IQ score of people with high lead levels.

We do not know the values of the population standard deviations.

Dependent Samples

Days of Release/Book Phoenix Prince
1 44.2 58.2
2 18.4 22.0
3 25.8 26.8
4 28.3 29.2
5 23.0 21.8
6 10.4 9.9
7 9.1 9.5
8 8.4 7.5
9 7.6 6.9
10 10.2 9.3
Critical Value:
Test Statistic:
p-value:

4. Write the hypotheses in symbolic form, determine if the test is right-tailed, left-tailed, or two tailed and explain why.

5. Calculate the critical value, the test statistic, and p-value. Show calculations below.

6. Make a decision about the null hypothesis and explain your reasoning, then make a conclusion about the claim in nontechnical terms.

Dependent Samples

The Harry Potter books and movies made a lot of money. A fan wanted to learn which of his favorite movies made more money. He collected the amounts grossed in millions during the first few days of releases of the movies Harry Potter and the Half-Blood Prince and Harry Potter and the Order of the Phoenix. Use a 0.05 significance level to test his claim that the Prince movie did better at the box office.

Use the p-value method to determine whether or not to reject the null hypothesis and state your conclusion.

Statistics homework help

Population Dynamics

Next, we will consider mathematical modeling of population dynamics. These models are heavily used in the
science of ecology and help us understand how populations interact with their environment and change over
time.

Take N(t) as the size of a bacterial population at time t. Suppose that the bacteria divide and produce new
bacterial cells at rate r per unit time. Then the population size at time t + ∆t is

N(t + ∆t) = N(t) + rN(t)∆t

Or

N(t + ∆t) −N(t)
∆t

= rN(r)

We take the limit as ∆t → 0 and get

dN

dt
= rN(t)

Next, we want to solve this model. Multiply both sides by dt and divide by N:

dN

N
= rdt

Integrate both sides

∫ t
0

dN

N
=
∫ t

0
rdt

or
ln N(t)|t0 = rt

ln N(t) − ln N(0) = rt

ln N(t) = ln N(0) + rt

N(t) = N(0)ert

This describes the growth of a population over time. N(0) is the population size at the initial time 0, r is the
population growth rate, and N(t) is the population at time t. Consider a population that starts at size 2 and
has a growth rate of 0.69 per year (the amount needed to double once per year):

1

N0=2
r<-c(1)
t=seq(from=0,to=100,by=0.1)
par(mfrow=c(1,1))
matplot(t,N0*exp(t(outer(r,t))),type=”l”,xlab=”time (years)”,ylab=”population size N(t)”,col=1:3,lty=1:3, main=paste(“exponential growth, r=”,r))

0 20 40 60 80 100

0
e

+
0

0
2

e
+

4
3

4
e

+
4

3

exponential growth, r= 1

time (years)

p
o

p
u

la
tio

n
s

iz
e

N
(t

)

#legend(“topleft”,c(paste(“r=”,r[1]),paste(“r=”,r[2]),paste(“r=”,r[3])),lty=1:3,col=1:3)

In 100 years, the population grows to size 1040. If this were a population of rabbits (who can easily reproduce
much faster than this), the mass of 1040 rabbits would be more than a billion times the mass of the sun.

Of course, populations cannot really grow infinitely. Instead, populations are regulated by resource limitations.

Discussion Questions

1. What resources put limits on human population growth? How about trees?

2. Make a plot of how you would expect the population growth rate to vary with population size.

2

Logistic Growth Model

A more realistic model of population growth must include resource limitations. One commonly used model is
the logistic growth model:

dN

dt
= rN(1 −

N

K
)

where

N is population size
r is the maximum population growth rate
K is the carrying capacity of the population. This is the maximum population that can be sustained given
the available resources.

The population growth rate in this model is

growth rate = r(1 −
N

K
)

When the population size N is small compared to the carrying capacity K, then we have N
K
≈ 0 and the

growth rate is approximately r:

dN

dt
≈ rN

In this case, the population grows approximately exponentially. As the population size increases, then the
population growth rate r(1 − N

K
) decreases.

r=1
K=1000
N=1:2000
growthrate=r*(1-N/K)

plot(N,growthrate,type=”l”,xlab=”population size N”, ylab=”population growth rate”, main=”population growth rate under logistic growth model”)

3

0 500 1000 1500 2000


1

.0

0
.5

0
.0

0
.5

1
.0

population growth rate under logistic growth model

population size N

p
o

p
u

la
tio

n
g

ro
w

th
r

a
te

We see that the population growth rate decreases linearly as the size of the population increases.

Discussion Question Make a plot of how you think that population will vary with time under the logistic
growth model starting at a low population size.

4

Solving the Logistic Growth Model

Unlike most population models, the logistic growth model actually has a solution:

N =
K

1 + K−N0
N0

e−rt

The plot below
r=0.69
K=1000
t=seq(from=0,to=20,by=0.1)

Nt=K/(1+(K-N0)/N0*exp(-r*t))

plot(t,Nt,type=”l”,xlab=”time (years)”, ylab=”population size N”, main=”logistic growth model with K=1000″)

0 5 10 15 20

0
2

0
0

4
0

0
6

0
0

8
0

0
1

0
0

0

logistic growth model with K=1000

time (years)

p
o

p
u

la
tio

n
s

iz
e

N

We see that the population grows smoothly to the carrying capacity. At this point, the population growth
rate is zero and so the population remains at the carrying capacity. At this point, birth and death are
balanced and the population is stably living within the available resources.

Let’s also solve this using the ODE solver:
library(deSolve)

## Warning: package ‘deSolve’ was built under R version 4.0.5

5

parameters<-c(r=0.69,K=1000) #specify model parameters
state<-c(N=1) #initial state of the population

LogisticGrowthmodel<-function(t,state,parameters)
{

with(as.list(c(state,parameters)),{

dN=r*N*(1-N/K)
return(list(c(dN)))

})
}

times<-seq(from=0,to=30,by=0.01)

logGrowthout<-ode(y=state,times=times,func=LogisticGrowthmodel,parms=parameters)

par(oma=c(0,0,3,0))
plot(logGrowthout,xlab=”time”,ylab=”population size N”, main=”logistc growth model from ODE solver”)

0 5 10 15 20 25 30

0
2

0
0

6
0

0
1

0
0

0

logistc growth model from ODE solver

time

p
o

p
u

la
tio

n
s

iz
e

N

We see that the dynamics look identical to the explicit solution, as we expect.

6

Human Carrying Capacity

The carrying capacity is the maximum population level that can be sustained by available resources.

If you google “human carrying capacity”, you can find many interesting resources. A good book on this topic
is How Many People Can the Earth Support by Joel Cohen. Here is an excerpt from Wikipedia:

Several estimates of the carrying capacity have been made with a wide range of population
numbers. A 2001 UN report said that two-thirds of the estimates fall in the range of 4
billion to 16 billion with unspecified standard errors, with a median of about 10 billion.[5]
More recent estimates are much lower, particularly if non-renewable resource depletion and
increased consumption are considered.[6][7] Changes in habitat quality or human behavior at
any time might increase or reduce carrying capacity. In the view of Paul and Anne Ehrlich,
“for earth as a whole (including those parts of it we call Australia and the United States),
human beings are far above carrying capacity today.”

The application of the concept of carrying capacity for the human population has been crit-
icized for not successfully capturing the multi-layered processes between humans and the
environment, which have a nature of fluidity and non-equilibrium, and for sometimes being
employed in a blame-the-victim framework. Supporters of the concept argue that the idea of
a limited carrying capacity is just as valid applied to humans as when applied to any other
species. Animal population size, living standards, and resource depletion vary, but the concept
of carrying capacity still applies. The number of people is not the only factor in the carrying
capacity of Earth. Waste and over-consumption, especially by wealthy and near-wealthy peo-
ple and nations, are also putting significant strain on the environment together with human
overpopulation. Population and consumption together appear to be at the core of many hu-
man problems.Some of these issues have been studied by computer simulation models such as
World. When scientists talk of global change today, they are usually referring to human-caused
changes in the environment of sufficient magnitude eventually to reduce the carrying capacity
of much of Earth (as opposed to local or regional areas) to support organisms, especially Homo
sapiens.

The carrying capacity is the population size at which the population is in balance with its resources and
thus can be sustained indefinitely. For humans, this is not a fixed value. It depends on technology, life styles,
etc. Consider the carrying capacity for the contemporary US versus England in the Middle Ages. We in
the US consume vastly more resources than someone living in the middle ages did. At the same time, our
technology and economic system is far more efficient and advanced. We are able to grow vastly more food on
the same amount of land and we are extremely good at extracting energy from our enivronment. Given this,
our currenty carrying capacity appears to be much higher than what it would have been 1000 years ago.

The human carrying capacity of around 10 billion cited in the Wikipedia entry above is primarly based
on food production. However, remember that carrying capacity means the population number that can be
sustained indefinitely. Our current prosper is based heavily on energy production. Enery production is based
heavily on fossil fuels. Fossil fuels are a non-renewable resource that is being exhausted quickly. The fossil fuel
supply may last 50 years or it may last 200 years, but will definitely run out. Our current farming practices
are energy dependent. Thus, much depends on whether we can transition to renewable energy recourses.

7

Stabiltiy Analysis of the Logistic Growth Model

We saw when used the ODE solver with the logistic growth that the population went smoothly to the
equilibrium with is available resources. Will this always happen?

Consider the model again:

dN

dt
= rN(1 −

N

K
)

We see that this has a steady states atN = 0 and N = K:

dN

dt
= 0 ⇒ rN̂(1 −

K
) = 0 ⇒ N̂ = 0 or N̂ = K

If the population moves slightly above N̂ = 0, then

dN

dt
> 0

Thus, the population increases away from 0. This is an unstable steady state.

If the population is slightly below the carrying capacity, then (1 − N
K

) > 0 and dN
dt

> 0.

If the population is slightly below the carrying capacity, then (1 − N
K

) < 0 and dN
dt

< 0.
That is, if we move slightly away from the steady state in either direction, we move back to the steady state.
Thus, it is a stable equilibrium.

The condition for stability is that the system return to the steady state point when we move away. That is,
dN
dt

> 0 for N < N̂
dN
dt

< 0 for N > N̂

In other words, the condition for stability is that the slope of the right hand side of dN
dt

is negative at N̂:

if dN
dt

= f(N), then the steady state N̂ is stable if df
dN

< 0.

In the case of the logistic growth model, we have

f(N) = rN
(
1 −

N

K

)
df

dN
= r
(
1 −

N

K

)
−rN

( 1
K

)
= r
(
1 −

2N
K

)
At N̂ = 0, we have

df

dN
= r
(
1 −

2 ∗ 0
K

)
= r > 0

This is always positive and so the steady state at N̂ is unstable. This is simple to understand. When N = 0,
then the population is at a steady state because there is no one in the population and thus it can’t grow. If
move away from the steady state, this means that there are now some individuals in the population. Because
the population is low, then the reproductive rate is high and the population grows exponentially away from
N = 0.

At N̂ = K, we have
df

dN
= r
(
1 −

2 ∗K
K

)
= −r < 0

8

This is always negative and thus the steady state is always stable.

Discussion Question

1. Under the logistic growth model, the population always goes smoothly to its carrying capacity. Do you
think that it this is realistic? That is, will populations always grow smoothly to equilibrium with their
resources?

2. Do you think that the model is a realistic depiction of a growing population? List the assumptions of
the model. What shortcomings does it have?

9

Discrete Time Models

In order to better understand what is going on, we will introduce discrete time model. Humans have
overlapping generations. That is, there are people many different ages alive and reproducing at the same
time. Thus, population growth is a continuous process. In contrast, many species have approximately
non-overlapping generations. For example, in many insect species, most of the population emerges over a
short time frame in the spring time, reproduces,and then dies. This produces a new generation, which are all
born around the same, reproduce all at about the same time, and then die. This cycle continues until winter.
For such species, it is reasonable to view time as progressing in discrete increments t = 1, 2, 3, ….

The discrete time logistic growth model is

N(t + 1) = rN(t)
(
1 −

N(t)
K

)
That is, each individual in generation t produces r

(
1 − N(t)

K

)
offspring.

Discrete time models are easier to handle computationally than continous time ones:
endtime=100 #length of time to simulate
N<-vector(length=endtime)
N[1]=20
r=1.2
K=1000

for(gen in 2:endtime) #loop over generations
{N[gen]=r*N[gen-1]*(1-N[gen-1]/K)
}

plot(1:endtime,N,type=”l”,xlab=”generations”, ylab=”population size”,main=”discrete logistic growth”)

10

0 20 40 60 80 100

5
0

1
0

0
1

5
0

discrete logistic growth

generations

p
o

p
u

la
tio

n
s

iz
e

Long-term Behavior of the Discrete Logistic Model

In the case above, with the population growth rate set to 1.2 (meaning each individual produces an average
of 1.2 offspring in the next generation), the population goes smoothly to an equilibrium.

The equilibrium occurs when N(t+ 1) = N(t) – that is, the population size doesn’t change between generations
t and t + 1. This gives

N(t) = rN(t)
(
1 −

N(t)
K

)
This is satisfied by

N̂ = 0

and

1 = r
(
1 −

K

)
or

N̂ = K(1 −
1
r

)

For the above example, we have r = 1.2 and K = 1000. This yields

11

N̂ = 1000(1 −
1

1.1
) = 166.67

If the population growth rate r < 1, then we have

N̂ = K(1 −
1
r

) < 0

This steady state does not exist if r < 1. In this case the population dies out because reproduction is below
replacement rate.
endtime=100 #length of time to simulate
N<-vector(length=endtime)
N[1]=20
r=0.5
K=1000

for(gen in 2:endtime) #loop over generations
{N[gen]=r*N[gen-1]*(1-N[gen-1]/K)
}

plot(1:endtime,N,type=”l”,xlab=”generations”, ylab=”population size”,main=”discrete logistic growth”)

0 20 40 60 80 100

0
5

1
0

1
5

2
0

discrete logistic growth

generations

p
o

p
u

la
tio

n
s

iz
e

If the population growth rate is between 2 and 3, there are dampled oscillations to the equilibrium:

12

endtime=100 #length of time to simulate
N<-vector(length=endtime)
N[1]=20
r=2.9
K=1000

for(gen in 2:endtime) #loop over generations
{N[gen]=r*N[gen-1]*(1-N[gen-1]/K)
}

plot(1:endtime,N,type=”l”,xlab=”generations”, ylab=”population size”,main=paste(“discrete logistic growth, r=”,r))

0 20 40 60 80 100

0
1

0
0

3
0

0
5

0
0

7
0

0

discrete logistic growth, r= 2.9

generations

p
o

p
u

la
tio

n
s

iz
e

If the population growth rate is above 3, we get cycles:
endtime=100 #length of time to simulate
N<-vector(length=endtime)
N[1]=20
r=3.2
K=1000

for(gen in 2:endtime) #loop over generations
{N[gen]=r*N[gen-1]*(1-N[gen-1]/K)
}

plot(1:endtime,N,type=”l”,xlab=”generations”, ylab=”population size”,main=paste(“discrete logistic growth, r=”,r))

13

0 20 40 60 80 100

0
2

0
0

4
0

0
6

0
0

8
0

0
discrete logistic growth, r= 3.2

generations

p
o

p
u

la
tio

n
s

iz
e

endtime=100 #length of time to simulate
N<-vector(length=endtime)
N[1]=20
r=4
K=1000

for(gen in 2:endtime) #loop over generations
{N[gen]=r*N[gen-1]*(1-N[gen-1]/K)
}

plot(1:endtime,N,type=”l”,xlab=”generations”, ylab=”population size”,main=paste(“discrete logistic growth, r=”,r))

14

0 20 40 60 80 100

0
2

0
0

4
0

0
6

0
0

8
0

0
1

0
0

0
discrete logistic growth, r= 4

generations

p
o

p
u

la
tio

n
s

iz
e

Time Delay and Overshooting the Resources

We see that as the growth rate gets higher, there are very large cycles. The population size goes far above its
carrying capacity and then crashes to very low levels. This happens because the population grows past its
available resources.

In the above run, the equilibrium is at

N̂ = 1000(1 −
1
4

) = 750

When the population reaches levels approaching 1000, then it is far past the sustainable level. Starvation
(our some other consequence, depending on the limiting resource) ensues and the population crashes.

When the population growth rate is higher, then the population is able to grow further beyond the resource
before consequences set in.

The reason why the discrete model displays this characteristic and the continuous one doesn’t is that in the
continious model the population growth rate responds instantaneously to the current resource level. In the
discrete model, there is a time delay between the population growth and the consequence of the population
growth.

Consider generations 22 to 30 in the above run
N[22:30]

## [1] 967.33704 126.38436 441.64542 986.37897 53.74198 203.41513 648.14966
## [8] 912.20671 320.34250

15

At generation 23, the population size is 126. It grows to 441 in the next generation and is still below carrying
capacity.Its growth rate is

r
(
1 −

N

K
) = 4(1 −

441
1000

)
= 2.236

It grows to 986 in the next generation and is now above carrying capacity. Now the growth rate is

r
(
1 −

N(t)
K

)
= 4
(
1 −

986
1000

)
= 0.056

That is, the population drops to 54 (5.6% of its current level) because it overshot its resources.

Discussion Question

We have seen that delay in response to resources leads to unstability cycles in population models.

1. What would cycles like the last plot mean in the context of human populations?

2. Do you think that there is time delay in human response to resources?

16

Time Delay in continuous Models

Consider the situation in generation 24 in the example above. At this point, the population is well below its
carrying capacity and resources are plentiful. For this reason, everyone in the population reproduces at a
high rate. Unfortunately, this leaves the next generation well above carrying capacity and so there is mass
starvation and population crashes.

This does not happen in the continuous logistic model because reproduction occurs continuosly and responds
instantaenously to the current resources. It is possible to build a time delay in resource reponse into a
continuous model. For example

dN

dt
= rN(t)

(
1 −

N(t− τ)
K

)
Thus, the current population growth rate depends on what the population was at τ time units in the past.
Typcially, current reproduction does not depend only on the current state. Rather, it depends on the whole
lifetime experience of the organism. For an animal, current reproduction may depend on its overall state
of health and its available energy reserves for making offspring (reproduction takes a lot of energy for the
female).

In the case of humans, we are consuming resources (e.g. energy, fresh water, soil quality) that we are barely
aware. Their depeletion will probably not affect our behavior until a crisis stage is reached. Thus, there is
clearly a time delay in our response to resourcesm, although much more complex than the simple model
above.

Time delay models are beyond the scope of this course. We can get the essential ideas from discrete models
much more simply.

17

Chaos

Note that as the population growth rate increases, the dynamics get increasingly complicated:

0 10 20 30 40 50

0
3

0
0

7
0

0

discrete logistic growth, r= 3

generations

p
o

p
u

la
tio

n
s

iz
e

0 10 20 30 40 50

0
4

0
0

discrete logistic growth, r= 3.3

generations

p
o

p
u

la
tio

n
s

iz
e

0 10 20 30 40 50

0
4

0
0

discrete logistic growth, r= 3.6

generations

p
o

p
u

la
tio

n
s

iz
e

0 10 20 30 40 50

0
4

0
0

1
0

0
0

discrete logistic growth, r= 3.9

generations

p
o

p
u

la
tio

n
s

iz
e

At r = 3.3, we have regular cycles. At r = 3.6, we can discern periodic behavior, but it is complicated. There
are four peaks in each cycle. At r = 3.9 there is not any discernable pattern. The behavior looks random.
Let’s look more closely:

18

0 10 20 30 40 50

0
2

0
0

4
0

0
6

0
0

8
0

0
1

0
0

0
discrete logistic growth, r= 3.9

generations

p
o

p
u

la
tio

n
s

iz
e

There is no periodic (repeating) dynamics. Instead, the dynamics look random. This behavior is known as
chaotic dynamics. Even though the system is completely deterministic (i.e. no randomness in the data), it
looks like random fluctuations. Consider the next plot, in which I run the system three times with slightly
different starting population sizes:

19

0 10 20 30 40 50

0
2

0
0

4
0

0
6

0
0

8
0

0
1

0
0

0
discrete logistic growth, r= 3.9

generations

p
o

p
u

la
tio

n
s

iz
e

N0=10
N0=11
N0=12

The only difference in the three lines is the starting population sizes of 10,11, and 12. We see that the
population dynamics are in sync at first, but quickly diverge. If we look at any point beyond about 20
generations, the populations are at radically different sizes even though they started out very similar.

Contrast this to the case with r = 3.3:

20

0 10 20 30 40 50

0
2

0
0

4
0

0
6

0
0

8
0

0
discrete logistic growth, r= 3.3

generations

p
o

p
u

la
tio

n
s

iz
e

N0=10
N0=11
N0=12

In this case the populations syncronize and after 20 generations that have identical dynamics.

The Butterfly effect

With r = 3.3, differences in the initial conditions dissapear with time.

With r = 3.9, differences in the initial conditions grow with time

This sensitivity to initial conditions is a hallmark of chaotic dynamics. With chaotic dynamics, tiny
differences in initial conditions lead to large differences later in. This is often called the butterfly effect: “a
butterfly flapping its wings in Chicago leads to a cyclone in the Indian Ocean”. This is an exagerration, but
the basic idea is true: in chaotic systems, tiny effects can lead to big differences in the outcome. These effects
are random for practical purposes and it is very hard to tell random dynamics from chaotic ones.

Chaotic dynamics are characterized by large, random-seeming fluctuations. The phenomenon was first
observed in models of weather and was later found to exist in many types of dynamical systems. In population
models, it tends too occur when population growth rates are large. Large population growth rates lead to
large population fluctuations and large fluctuations lead to chaos.

Does Chaos Happen in Real Populations?

Chaos readily occurs in models, but does it occur in real populations? There has been a great deal of interest
in this question. Consider Figures 1 and 2 below. These show scatter plots of estimates of the Lyapunov
number for a selection of laboratory (Figure 1) and field (Figure 2) populations.

21

Figure 1: Figure from Ellner and Turchin, American Naturalist, 1995, vol 145(3)

The only thing that you need to know about the Lyapunov number is

γ < 1 ⇒ non-chaotic dynamics

γ > 1 ⇒ chaotic dyamics

We see from the figures that very few populations appear to exhibit chaotic dyamics. However, many
populations are right at the boundary of chaos.

Evolution of Population Dynamics

Why should it be that many populations are at the boundary of chaos? The answer to this is unknown.
However, we can speculate as to the reason.

Evolution works on reproduction. When a trait leads to higher survival and reproduction, then it is favored by
evolution and tends to spread in a population. All else being equal, it is beneficial to an organism to produce
more offspring. Of course “all else” is usually not equal and there are complex tradeoffs in determining the
optimal strategy for an organism in terms of reproduction. Still, producing more offspring will often be a
beneficial strategy and thus evolution will often favor it.

22

Figure 2: Figure from Ellner and Turchin, American Naturalist, 1995, vol 145(3)

23

This leads to a problem: Evolution works on individuals. An individual’s evolutionary interests are often
best served by maximizing the number of offspring. However, high reproduction leads to unstable population
dynamics, which is bad for the population.

Large fluctuations in population numbers can easily lead to population extinction. When the population
number gets very low, some chance event (disease, bad weather, etc) can kill enough of the remaining
members that the population goes extinct. Thus, natural selection on individuals may lead to extinction of
the population.

This leads to multiple hypotheses about why we see many populations at the boundary of chaos, but few over:

1. Populations that cross the boundary into chaos tend to become extinct. Thus, the distribution of
Lyapunov numbers that we observe is the result of a distribution of optimal individual reproductive
numbers. However, the high end of the distribution gets truncated by population extinction.

2. Evolution favors being at the edge of chaos. That is, it might be most beneficial to have the highest
reproductive rate that doesn’t lead to chaos. Thus, natural selection would favor reproductive rates
right at the boundary. However, although this seems intuitively appealing, it has a major problem:
Natural selection works on individuals, not groups. Suppose that we are in a situation where the average
reproductive rate in the population is just below the threshold for chaos. An individual would still
benefit by producing more offspring. If some individal has a mutation that leads to more offspring, then
that mutation will tend to be represented more in future generations and it will thus spread and lead
to higher reproductive rates. Even though the population as a whole will better off if each individual
limits reproduction, individuals gain short-term benefit by “cheating” and reproducing more. Various
researchers have suggested ways in which individual natural selection could lead to stable population
dyanamics (my very first scientific publication was on this topic), but it remains an open question.

24

Dynamics of Multiple Populations: Predator-Prey Interactions.

Figure 3 shows a famous data set in population ecology. This shows the number of hare and lynx pelts
traded by the Hudson Bay Company over a period of 100 years. We see a strong cyclic pattern in both
populations, with a period of about 10 years. The lynx cycle lags behind the hare cycle by perhaps 1-2 years.
The lynx is a major predator of the hare and the hare is a major food source for the lynx. The explanation
for the observed pattern is that 1) in absence of many lynx, the hare population increases rapidly; 2) as the
hare population increases, the lynx population also increases because there is plentiful food for the lynx; 3)
As the lynx population begins to get large, they eat too many hare and the hare population collapses; 4)
When the hare population collapses, the lynx population collapses soon after because there is not enough
food; 5) Once the lynx population collapses, the hare population then starts to increase again. 6) Repeat.
Ecologists are interested in understanding what drives these dynamics. There has been a large amount of
work in developing mathematical models for population dynamics and then fitting these models to data.

Assumptions

Take X to represent the prey (e.g. hare) population number and Y to represent the predator (e.g. Lynx)
population number.

We will assume
1. In absence of predators, the prey population follows the logistic growth model (and thus follows the
assumptions of that model).
2. The prey is the only food source for the predator. Thus, in absence of the prey, the predator population
decreases at rate r2.
3. The prey has only one predator.
4. The loss in prey biomass due to predation is given by α1XY1+βX . This will be explained below.
5. The gain in predator biomass due to predation is given by α2XY1+βX .
6. There is no randomness in the amount of reproduction, predation, etc.
7. The enivronment is constant. There are no changes in prey resource availability, mortality, etc.
8. There is no structure to either population. There is no variation due to age, sex, genetics, location, etc.

25

With these assumptions, we have

dX

dt
= r1X

(
1 −

X

K

)

α1XY

1 + βX

dY

dt
= −r2Y +

α2XY

1 + βX

r1
(
1 − X

K

)
is the growth rate of the prey population in absence of the predator (logistic growth)

−α1XY1+βX is the decrease in the prey biomass due to predation

−r2Y is the is the (negative) growth rate of the predator population in absence of the prey (they die out
with no food).
α2XY
1+βX is the increase in predator biomass due their predation on prey.

Functional Response

The term α2XY1+βX is called the functional response. This determines the amount of prey eaten as a function
of prey density.

The function that we use here is called a Holling Type II functional response. Holling was a scientist who did
early work on the concept of functional response. Plot the function:
maxX=100 #max number of pret eaten
halfmax=50 #prey number at half max eaten

beta=1/halfmax
alpha=beta*maxX

X=seq(from=0,to=1000,by=1)
plot(

Statistics homework help

Project #1 Hints

Here are some hints about how I have done my version of Project #1. You do NOT need to do things
exactly like me. I am just showing some things that have worked well for me.

First of all, my pop data frame is structured as follows:

Diseas
e
Status

Age
(days)

Household

Workp
lace/
School

Job/
grade

Day of
recove

r

Day of
death

Long
COVID

0 11278 1 LB6 17 -10 -10 0
0 7828 1 NW 537 -10 -10 0
0 27517 2 SB91 5 -10 -10 0
0 14830 2 SB195 2 -10 -10 0
0 8886 3 SB144 3 -10 -10 0
0 22095 3 SB127 2 -10 -10 0
0 1883 3 SC -1 -10 -10 0
0 1902 3 SC -1 -10 -10 0
0 27091 4 LB4 47 -10 -10 0
0 20680 4 LB10 22 -10 -10 0
0 1497 4 SC -2 -10 -10 0
0 20547 5 NW 833 -10 -10 0
0 20894 5 SB166 2 -10 -10 0
0 12214 5 LB2 20 -10 -10 0
0 16778 5 NW 420 -10 -10 0

The column Household tells which household each person belongs to. This is how I know who is in the
same household. Likewise, the column Workplace/School shows where each person works and this is
how I know who works together. The Job/grade column corresponds to jobs slots for adults and grade in
school for children. Each workplace has a number of available job slots and this tells which slot each
person has. At present, my program does not use this. I included it in case I wanted it in the future. The
school grade is calculated for each student based on their age. It is negative for kids not in school yet. I
use the grades to determine which kids are exposed to each other. Day of recovery and Day of death are
the days when a person sick with COVID will either recover of die. This is determined when they are
infected. These values are initially set to negative numbers to indicate that the person has not been
infected. The Long COVID column is 1 if an individual gets long COVID.

Setting up the population

My function to set up the population has the following as its core:

pop=NULL
Loop (f over households){
X=runif(1)
If(x<0.25){ #single invidual

pop=rbind(pop,c(0,adult_age(),f,NA,NA,-10,-10,0))
} else if ((x>0.25)&(x<0.35){ #two adults with no kids
pop=rbind(pop,c(0,adult_age(),f,NA,NA,-10,-10,0))
pop=rbind(pop,c(0,adult_age(),f,NA,NA,-10,-10,0))
} else if
.
.
.
.

}

This does a loop over households. For each household, it generates random number x to figure out what
type of household it is. The series of if/ifelse steps correspond to the different possibilities for the
household type. The lines pop=rbind(pop,c(0,adult_age(),f,NA,NA,-10,-10,0)) add individuals into the
population. Each time that I had someone in, there is a line like this. The first option adds one adult, the
second adds two adults. Further options add individuals for other household options. This sets the initial
values for each individual. I fill in jobs/school later, so everyone is set to NA initially for these. f is the
index for the current household.

Statistics homework help


1

Advertising Age annually compiles a list of the 100 companies that spend the most on advertising. Consumer-goods company Procter & Gamble has often topped the list, spending billions of dollars annually. The data on annual advertising expenditures for a sample of 20 companies in the automotive sector and 20 companies in the department store sector are contained in the Excel Online file below. Construct a spreadsheet to answer the following questions.

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2

The Russell 1000 is a stock market index consisting of the largest U.S. companies. The Dow Jones industrial Average is based on 30 large companies. The data giving the annual percentage returns for each of these stock indexes for 25 years are contained in the Excel Online file below. Construct a spreadsheet to answer the following questions.

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3

The Russell 1000 is a stock market index consisting of the largest U.S. companies. The Dow Jones industrial Average is based on 30 large companies. The data giving the annual percentage returns for each of these stock indexes for 25 years are contained in the Excel Online file below. Construct a spreadsheet to answer the following questions.

Graphical user interface, text, application  Description automatically generated

Table  Description automatically generated

4

The average waiting time for a patient at an El Paso physician’s office is just over 29 minutes, well above the national average of 21 minutes. In fact, El Paso has the longest physician’s office waiting times in the United States. In order to address the issue of long patient wait times, some physician’s offices are using wait tracking systems to notify patients of expected wait times. Patients can adjust their arrival times based on this information and spend less time in waiting rooms. The Excel Online file below contains the data showing wait times (minutes) for a sample of patients at offices that do not have an office tracking system and wait times for a sample of patients at offices with an office tracking system. Construct a spreadsheet to answer the following questions.

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Table  Description automatically generated

5

Naples, Florida, hosts a half-marathon (13.1-mile race) in January each year. The event attracts top runners from throughout the United States as well as from around the world. 22 men and 31 women entered the 19-24 age class. Finish times in minutes are contained in order of finish in the Excel Online file below. Construct a spreadsheet to answer the following questions.

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Outliers in the women’s group. _____

Statistics homework help

Please type your answer in RED on this same file. Don’t use handwriting on a paper, do not use PDF file.

Make sure you type your name

**Show the steps of the calculations, don’t just give me the answer,

**Show 1 or 2 decimal and unit of the answer.

NAME:

(1) In 2021, there were 71,948,100 women of childbearing age nationwide. There were 5,130,600 live births, what is the fertility rate per 1,000 women of childbearing age.

(2) During the last 2 years, there were 47,115 COVID infections in the town, 3,185 patients were sympathetic. What is the annual rate of sympathetic per 100,000 population?

(3) In last month, the total length of COVID inpatient stay was 2,128 days, and the number of discharges was 265, what is the average length of stay (ALOS)

(4) A well-baby nursey unit records the following statistics in January :

Newborn bed count 25 Discharges 220 1

Newborn service days 428 Newborn discharge days 435

Calculate:

(a) Average length of stay for well-baby newborns in January

(b) New born baby bed Occupancy rate for well-baby nursey unit in January

(5) A total of 5 newborn died during December and there were 232 live newborn discharges. What is the newborn death rate?

(6) If a total of 500,000 people are alive with a diagnosis of diabetes in the year the US population was recorded at 310 million. What is the prevalence rates

(a) per 1,000,

(b) per 100,000.

(7) Ten Year ago, the number of incidence of AIDS was 25,700 in the US when the population in the middle of the year was reported as 290 million. What is the new cases of AIDS per 100,000 population during that year?

(8) The estimated population of a state during the past year is 22 million. The total cancer deaths during the same year were 4,500.

What is the death rate

(a) per 1,000 population,

(b) per 10,000?

(9) The pediatric unit of a hospital has 20 beds. Last week, the IP service day totals were 12,11,13,9,10,13,7. What is the occupancy percentage for last week?

(10) the last whole year (using 365.25 days), a hospital has 350 inpatient beds, the bed occupancy rate was 92%, an average length of stay was 7.5 days.

How many times of the 350 beds changed occupants in the last whole year.

Statistics homework help

lease read the scenario below, and then answer the questions that follow in a 3-page analysis. The questions will guide your analysis of the situation, but they need to be presented as part of a report to the owner of the company.

Scenario:

Dancin’ Donuts, established in January 2019, is a thriving new business specializing in low-carb donuts. The 2019 keto diet fad led to increased sales, and the chief financial officer (CFO) prepared a robust budget for 2020. In early March 2020, the small business had record-breaking sales but abruptly needed to shut its doors because of the global pandemic. The CFO conducted the following analysis for the month of March:

Dancin’ Donuts March 2020

 

 

 

 

 

 

 

 

 

Budget

Actuals

$ Var

%

 

Total Revenue

200,000

196,947

-3,053

-2%

 

Total Cost of Goods Sold

100,000

98,000

-2,000

-2%

 

GROSS PROFIT

100,000

98,947

-1,053

-1%

 

 

 

 

 

 

 

 

 

 

Total Expense

75,000

72,000

-3,000

-4%

 

 

 

 

 

 

 

 

 

 

 

Total Interest Income

200

100

-100

-50%

 

 

Total Other Expense

1,000

1,000

0

0%

 

 

 

 

 

-800

-900

-100

13%

 

 

 

 

 

 

 

 

 

Earnings Before Interest, Taxes, Depreciation, & Amortization (EBITDA)

24,200

26,047

1,847

8%

 

 

Total Interest Expense

6,400

6,385

-15

0%

 

 

Total Depreciation & Amortization

10,000

10,000

0

0%

Earnings Before Taxes (EBT)

7,800

9,662

1,862

24%

 

 

 

 

 

 

 

 

 

 

 

Total Income Taxes (30%)

2,340

2,899

559

24%

 

 

 

 

 

 

 

 

 

Net Income

5,460

6,764

1,304

24%

Please answer the following questions:

1. What does AVB stand for?

2. What is the total revenue for March 2020 when compared to the budget?

3. What is the variance from the budget in the net income for the month?

4. What is the income tax percentage for the month?

Submitting your assignment in APA format means, at a minimum, you will need the following:

· Title page: Remember the running head. The title should be in all capitals.

· Length: 3 pages minimum

· Body: This begins on the page following the title page and abstract page and must be double-spaced (be careful not to triple- or quadruple-space between paragraphs). The typeface should be 12-pt. Times Roman or 12-pt. Courier in regular black type. Do not use color, bold type, or italics, except as required for APA-level headings and references. The deliverable length of the body of your paper for this assignment is 3 pages. In-body academic citations to support your decisions and analysis are required. A variety of academic sources is encouraged.

· Reference page: References that align with your in-body academic sources are listed on the final page of your paper. The references must be in APA format using appropriate spacing, hanging indent, italics, and uppercase and lowercase usage as appropriate for the type of resource used. Remember, the Reference page is not a bibliography but a further listing of the abbreviated in-body citations used in the paper. Every referenced item must have a corresponding in-body citation.

Statistics homework help

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* * **

Introduction*and*Demonstration*of*SPSS

Introduction*and*Demonstration*of*SPSS
Program Transcript

MATT JONES: Hi, my*name is*Dr. Matt Jones*and I’m a quantitative
methodologist. And today*I’m here to give you a brief introduction and tutorial to
SPSS. There are two sides*to SPSS, the Data View and the Variable View. If you
look*down at the bottom*of the screen where my*cursor*is, you’ll see that the data
view is*currently*highlighted. These are the raw values*for*the data for*each case
for*each respondent in this*particular*database.

If we click*on the Variable View the screen takes*us*over*to the information about
all of the variables*in our*dataset. The first column is*the Variable Name. And this*
is*the name that is*given to each variable in SPSS.

The second column tells*us*what type of variable it is. Typically*for*most of our*
basic*data analysis, we will be dealing with numeric*variables. If we move over*to
the Label column, which can be expanded by*just placing your*cursor*over*at the
top, and expanding or*either*minimizing, this*provides*us*the label or*the
description in quote, unquote “plain English”*for*each of the variables.

It’s also important to note the values*for*each specific*variable. If you click*on the
Value Box, a little gray*box*is*highlighted next to it. If you go ahead and click*on
that, it will open up another*window. Here you will see the value labels*for*each
value.

Here we can see each variable is*coded with values*of 0, 1, 2, 8, and 9. In this*
case for*this*data set, a value of 0 equals*in applicable 1 equals*yes, 2 equals*no,
8 equals*don’t know, and 9 equals*no answer. You can go ahead and cancel that
box.

If you click*on missing cells, a little gray*box*is*highlighted off to the right. Go
ahead and click*on that, and that brings*up discrete missing values*for*this*
specific*variable. Here you can see that the discrete missing values*of 0, 8, and 9
are coded as*being missing.

It’s important to note this*information because these values*will not be used in
any*statistical analysis*within the set. If we hit Cancel and go back*to our*values*
we can see that those specific*values*of 0, 8, and 9 reference inapplicable, don’t
know, or*no answer. Therefore, they*will not be used in analysis*and treated as*
missing data.

It’s also important to note the column Measure. There are three options*here,
scale, ordinal, and nominal. This*refers to the level of measurement for*that
specific*variable. It’s important that these be accurately*entered because SPSS*
will not perform*some functions*because it makes*assumptions*about levels*of
measurement for*certain procedures.

©2016 Laureate*Education, Inc. 1

*

* * *

* * * * * * * * * * * * *
* * * * * * * * * * * * * * *
* * * * * * * * * * * *

* * * * * * * * * *
* * * * * * * * * * *

* **

* * * * * * * * * * * * * *
* * * * * * * * * * * * *

* * * * * * * * **

* * * * * * * * * * * *
* * * * * * * * * * *

* * **

*

Introduction*and*Demonstration*of*SPSS

You could also obtain variable information by*going to the top of the screen,
clicking on Utilities, and clicking on Variables. Off to the left hand side of the
screen you’ll see a list of all the variables*within the specific*dataset. The
information to the right tells*you specifically*about the variable. The variable
name, the label, the missing values, its*level of measurement, and the labels*for*
that specific*value.

You can choose any*variable within this*data set, and it will provide you with that
specific*information. You can also click*on Go To, which will take you to that
specific*variable. Here you will see that that variable is*highlighted.

And that’s a quick*overview of the two sides*of SPSS, Data View and Variable
View. If you have further*questions, be sure and utilize your*textbook*and also
your*instructor*as*a valuable resource.

©2016 Laureate*Education, Inc. 2

Statistics homework help

Consider a study designed to assess the association between obesity, defined as a body mass index (BMI) of 30 and more and the incidence of cardiovascular disease. Data are collected in a cohort study in which participants ages 35 and 65 who were free of cardiovascular disease (CVD) are enrolled and followed over 10 years. Each participant’s BMI is assessed at baseline and particxipants are followed for 10 years for incident cardiovascular disease. A summary of the data are given below:

Incident CVD No CVD Total

Obese 46 254 300

Not obese 60 640 700

Total 106 894 1000

Statistics homework help

Infectious Disease Dynamics with Immunization

Age Structure

The final thing that we will do with epidemic models is to study the effect of immunization. In order to do
this, we will need a model that has age structure. Our previous models do not track age. They treat everyone
as identical in the population. Howeer, the dynamics of vaccination are highly dependent on age structure.

We can write differential equation models that include age structure. However, this would require (partial
differential equations). This a more advanced area that we won’t study in this class. Instead, we will modify
the simulation model.

Previously, the population was represented with a vector pop that stored the disease status (susceptible,
infected, recovered) for each member of the population. Now, we will represent the population with a matrix,
that stores disease status, age, age at infection, and sex:

The function below initializes the population:
#function that generates poisson(lambda) values until it gets a non-zero value
trunc_pois<-function(lambda)
{ d=0

while(d==0) d=rpois(1,lambda)
return(d)

}

FindWorkPlace<-function()
{

}

#Make random households
#F0 fanilies with kids. All have two parents, make and fenale
#S0 households adults only of random size

make_households<-function(pop,H0)
{ for(f in 1:F0)

{ ageM=runif(20,50) #qge of mother
ageD=ageM+rnorm(0,5) #age of father
nKids=trunc_pois(1)

mom=c(0,ageM,NA,1,f,)

}

1

}

initialize_pop<-function(S0,I0,maxAge)
{#initialize the population. pop0 is matrix with pop0[i,1]=susceptble/infected/recovered status

#pop0[i,2] is current age. pop0[i,3] will be assigned age at infection, pop0[i,4]=1 if female

pop0=matrix(nrow=S0+I0,ncol=4)

#assigned susceptible/infected status:
pop0[1:S0,1]=0
pop0[(S0+1):(S0+I0),1]=1
pop0[(S0+1):(S0+I0),3]=0 #assign age at infection

#assign ages. all ages have equal probability.
pop0[,2]=sample(maxAge*365,S0+I0,replace=T)

#assign sex (only females reproduce)
pop0[,4]=ifelse(runif(nrow(pop0))<=0.5,1,0) #1 if female, 0 if male

return(pop0)

}

Now, we can have important parameters (infection rates, death rates, etc) vary by age. The functions nelow
define age-specific rates. Each function takes age a as input and outputs the appropriate rate. Note that
these currently are not very realistic. I didn’t use any data in setting the rates and instead just took very
simple values. However, we can easily incorporate detailed data.
InfectionRatebyAge<-function(a)
{ #function returns the infection rate for an individual of age a

# age is in days

if(a<=5*365) { #less than 5 years old
return(0.015)
} else if(a<=10*365) { #5-10 years old

return(0.012)
} else if(a<=69*365) {#10-69 years old

return(0.01)
} else{ #> 69

return(0.02)
}

}

RecoveryRatebyAge<-function(a)
{ #function returns the infection recovery rate for an individual of age a

# age is in days

2

if(a<=5*365) {
return(0.1)

} else if(a<=10*365) {
return(0.1)

} else if(a<=69*365) {
return(0.1)

} else{
return(0.1)

}

}

BirthRate<-function(a)
{#function returns the birth rate for an individual of age a

# age is in days
#currently set so that women from 18 to 45 have same fertility rate
#if less than 18 or more than 45, fertility is zero.
#this is not very realistic. We can improve with data
if(a<=18*365){

return(0)
} else if(a<=45*365) {

return(1/27)
} else {

return(0)
}

}

BackgroundMortalitybyAge<-function(a)
{ #function returns the infection rate for an individual of age a

if(a<=5*365) {
return(0.015/365)

} else if(a<=10*365) {
return(0.015/365)

} else if(a<=69*365) {
return(0.015)

} else{
return(0.05/365)

}

}

The functions below do all do the updating of the population. The functions infect, recover,
backgroundmortality, and birth work similarly to how they did previously. However, they are now
modified to account for age structure. The functions aging, clear_dead and cap_pop are new: aging ages
the population by one day every day andclear_dead removes dead people from the population each day.
The function cap_pop puts a cap on the population. If the population exceeds maxpop at the end of the day,
then the function randomly selects people and removes them from the population. This function is required
to prevent the population from growing exponetially and making the program run very slowly. Ideally, we
would have death rates and birh rates balanced so that the population stays constant. However, this is
difficult to acheive in practice and so we force a cap on the population.

3

aging<-function(pop)
{#function to age everyone by one day

pop[,2]=pop[,2]+1

}

#Function to make new infections:
#”flips coin” for each population individual to see whether they get the disease.
#if so, their status is changed from susceptible (0) to infected (1).
infect<-function(pop,InfectRate)
{ nI<-sum(pop[,1]==1) #number of infecteds

nS<-sum(pop[,1]==0) #number of susceptibles
pop1=pop #create copy of pop

susceptibles=which(pop[,1]==0) #make vector giving positions of suscepibles

beta=sapply(pop[susceptibles,2],InfectRate) #sapply applies the function to the vector
#produces a vector of infection probabilities.
#where beta[i] is infection prob for ith susceptible

pi=1-(1-beta)^nI #probility of susceptible being infected. Calcs seperate prob for each individual, based on
# that individuals age-specific infection prob.

#pi=ifelse(beta*nI<=1,beta*nI,1)

pop1[susceptibles,1]=ifelse(runif(nS)<pi,1,0) #check if each susceptible becomes infected

return(pop1)
}

#function to make individuals recover
#”flips coin” for each infected individual to see whether they recover from the disease.
#if so, their status is changed from infected (1) to recovered.
recover<-function(pop,RecRate)
{

nI<-sum(pop[,1]==1) #number of infected
pop1=pop

infecteds=which(pop[,1]==1)

gamma=sapply(pop[infecteds,2],RecRate) #sapply applies the function to the vector
#produces a vector of infection probabilities.

pop1[infecteds,1]=ifelse(runif(nI)<gamma,2,1) #check if each infected recovers. This is the “coin flip”

return(pop1)

4

}

#function to check whether each individual dies from non-disease causes
#MortRate is a function that gives the mortality rate for each age
backgroundmortality<-function(pop,MortRate)
{

pop1=pop
n=nrow(pop1) #current population size

#note that this doesn’t distinguish between living and dead. That is, dead people can die again. This does not
#affect anything.

nu=sapply(pop[,2],MortRate) #produces a vector of mortality rates for everyone in the population
#This is speficic to their age

pop1[,1]=ifelse(runif(n)<=nu,3,pop1) #check if each person dies . If so, write 3, if not write current value

return(pop1)

}

#function to check whether each individual dies from disease
diseasemortality<-function(pop,m)
{

nI<-sum(pop==1) #number of infected
pop1=pop
pop1[pop==1]=ifelse(runif(nI)<=m,3,1) #check if each infected dies

return(pop1)
}

birth<-function(pop,birthrate)
{ #function to check for births

#birthrate is a function that gives fertility rate by age.

females<-pop[pop[,4]==1,] #find the females
nf<-nrow(females) #number of females

nbaby<-sum(runif(nf)<sapply(females[,2],birthrate)) #number of babies born today

if(nbaby>0) #if any babies are born today, then add them to the population
{ babies<-matrix(nrow=nbaby,ncol=4)

babies[,1]=0 #babies born susceptible (ignoring possibility of temporary immunity from mother)
babies[,2]=0 #age 0
babies[,4]=ifelse(runif(nbaby)<=0.5,1,0) #assign sex
return(rbind(pop,babies))

}

return(pop) #if no babies, then return pop as is

5

}

clear_dead<-function(pop)
{#function to remove dead from population

return(pop[-which(pop[,1]==3),])
}

cap_pop<-function(pop,maxpop)
{#this function caps the population. If the population size exceeds maxpop, it randomly selects (n-maxpop) individuals
# and removes them from the population

n<-nrow(pop)

if(n<=maxpop) return(pop)

remove<-sample(1:n,(n-maxpop),replace=F)

return(pop[-remove,])

}

Finally, here is the main program. This follows the same format as the model without age structure, but
with functions that account for age structure.
#initialize the population
pop=initialize_pop(S0,I0,max_age)

#initialize the output variables:
St=S0
It=I0
Rt=0
Mt=0
At=NULL
Vt=0
Qt=NULL
RI=NULL #will store proportion of

#this is the main part of the program. This loops over time. Each time step is one day. On each day, it checks whether each
#person has caught the disease, recovered from the disease, died from non-disease causes, died from disease, or had a baby.
for (time in 1:endtime)
{ if(time/(10*365)==floor(time/(10*365))) print(time/365) #print time every ten years to track progress

pop=infect(pop,InfectionRatebyAge)
pop=recover(pop,RecoveryRatebyAge)
pop=backgroundmortality(pop,BackgroundMortalitybyAge)
pop=diseasemortality(pop,m)
pop=birth(pop,BirthRate)
pop=aging(pop)

6

St=c(St,sum(pop[,1]==0))
It=c(It,sum(pop[,1]==1))
Rt=c(Rt,sum(pop[,1]==2))
Mt=c(Mt,sum(pop[,1]==3))
At=c(At,mean(pop[,3],na.rm=T))
Vt=c(Vt,sum(pop[,5]==1))

#Qt=c(Qt,St*mean(sapply(pop[,2],InfectionRatebyAge))/mean(sapply(pop[,2],RecoveryRatebyAge)))

pop=clear_dead(pop)
pop=cap_pop(pop,maxpop)

if(time/(10*365)==floor(time/(10*365))) if(sum(pop[,1]==1)<1) pop[1,1]=1 #if infected drops below 1 add 1 every ten years.

}

Here is a run of the model with age structure. We see that it goes through large amplitude cycles, with
disease outbreaks about once every 20 years. In each outbreak, most of the population is infected (we can
tell this because the number of susceptibles gets close to zero). The cycles are irregular both in amplitude
and period, suggesting the possibility of chaotic dyanmics (we will discuss chaos in the context of population
dynamics, our next topic). They don’t show any sign up damping over the 1000 years plotted (in fact, I ran
it for 2000 years total and there was not sign of damping over that range either). I am not sure why the
cycles are so much bigger with the age stuctured population.

7

0 200 400 600 800 1000

0
5

0
0

1
5

0
0

2
5

0
0

time (years)

n
u

m
b

e
r

Susceptible
Infected
Recovered

Immunization

Next, we will consider the effect of immunization.

From Wikipedia:

A vaccine is a biological preparation that provides active acquired immunity to a particular disease. A vaccine
typically contains an agent that resembles a disease-causing microorganism and is often made from weakened
or killed forms of the microbe, its toxins, or one of its surface proteins. The agent stimulates the body’s
immune system to recognize the agent as a threat, destroy it, and to further recognize and destroy any of the
microorganisms associated with that agent that it may encounter in the future. Vaccines can be prophylactic
(example: to prevent or ameliorate the effects of a future infection by a natural or “wild” pathogen), or
therapeutic (e.g., vaccines against cancer are being investigated).

The administration of vaccines is called vaccination. Vaccination is the most effective method of preventing
infectious diseases; widespread immunity due to vaccination is largely responsible for the worldwide eradication
of smallpox and the restriction of diseases such as polio, measles, and tetanus from much of the world. The
effectiveness of vaccination has been widely studied and verified; for example, the influenza vaccine, the HPV
vaccine, and the chicken pox vaccine. The World Health Organization (WHO) reports that licensed vaccines
are currently available for twenty-five different preventable infections.

The widespread adoption of vaccines has greatly reduced the incidence of many diseases. Smallpox, formerly
one of the largest killers of humans, has been completely eradicated from the world (there are samples at two
locations in the world: the CDC in Atlanta, and a government lab in Russia).

In the case of measles, there were an estimated 2-3 million deaths world wide each year before the vaccine was
introduced. That number has dropped to under 100,000 per year (e.g. an estimated 90,000 measles deaths in

8

2016). These deaths are predominantly in developing countries where there are not widespread immunization
programs.

In the US, there were 700,000 measles cases in the US in 1958 (before the adoption of the measles vaccine),
resulting in 558 deaths. Since the vaccine came into wide use, the number of cases dropped to under 100 per
year (Figure 1).

The table in Figure 2 summarizes measles cases in 2008:

9

reference:https://www.cdc.gov/mmwr/preview/mmwrhtml/mm5718a5.htm

We see that most cases were from unvaccinated cases. Although measles is very rare in the US, it is still
fairly common in some developing countries. All or nearly all outbreaks in the US start with people traveling
from other countries.

Figure 4 below shows measles in recent years (source=CDC). Unfortunately, measles has been on the increase
because of the unfortunate trend of parents not vaccinating their children.

Vaccine Schedule

In order to maximize protection, it is recommended that children be vaccinated as soon their immune
system is sufficiently developed to respond to a particular vaccine. This has led to a complicated schedule of
recommended ages for vaccinations. The link below shows the schedule for the US.

10

https://www.cdc.gov/vaccines/schedules/hcp/imz/child-adolescent.html

Children in the US typically receive the vaccines during their regularly checkups at the pediatrician. The
pediatrician cannot force children to get vaccines. However, all 50 states have laws requiring children to be
vaccinated before entering kindergarten in public schools.

Unfortunately, there has been a trend towards parents not vaccinating their children in the US and other
western countries. This is based on 1) mistaken beliefs about the safety of vaccines and 2) people not under-
standing how devastating these diseases once were for children before vaccines were introduced. Fortunately,
most parents still get their children vaccinated and these diseases are largely kept in check. However, there
have been outbreaks of measles, whooping cough, and other diseases in parts of the country where large
numbers of parents don’t vaccinate their kids.

We will apply immunization using the function below. For simplicity, we assume that children are vaccinated
exactly on their 5th birthday. We define a vaccination rate ir. On each child’s 5th birthday, we “flip the
coin” to determine if they are vaccinated. If so, there disease status is changed to 2. The status of 2 formerly
represented recovered. Now it represents immune whether by recovering from the disease or from vaccination.
We assume that the vaccine is 100% effective and that immunity is never lost.
immunize<-function(pop,ir)
{ #function to immunize. Assumes that kids are immunized exactly on their five-year-old birthday

#ir is immunization rate

immunize_today<-which(pop[,2]==365*5) #find kids with 5-year-old birthday today
nb<-length(immunize_today) #number of kids with 5-year old birthday today

if(nb>0) #if there are any with 5-year birthday today, then check whether immunuized.
{ pop[immunize_today,]=ifelse(runif(nb)<ir,2,pop[immunize_today,]) #if vaccinated, then change status to immunized
} #else leave as is

return(pop)

}

Here is a run with 90% of children immunized at age 5. The model runs for 100 years before the immunization
program begins. Because only 5-year-olds are vaccinated, it takes decades before a large portion of the
population is immunized. Once this happens, the disease outbreaks are greatly reduced. After the introduction
of the vaccine, there are three outbreaks in 200 years. All three are of much smaller magnitude than what
was observed before the vaccine was introduced.

11

0 50 100 150 200 250 300

0
5

0
0

1
0

0
0

2
0

0
0

90% immunization at age 5

time (years)

n
u

m
b

e
r Susceptible

Infected
Recovered/Immune
vaccinated

Next, let’s see what happens as the proportion vaccinated is decreased. The next plot shows the same run,
but with vaccination rates of 80% rather than 90%. Now we see that the disease outbreaks are larger in
magnitude and possibly more frequent. It is easier to see the magnitude of the outbreak in the changes in the
number of susceptibles than in the number infected. There are four large outbreaks after the introduction of
the vaccine. These are much smaller in magnitude than the pre-vaccine (Where nearly everyone was infected),
but still there are large numbers of people getting the disease.

12

0 50 100 150 200 250 300

0
5

0
0

1
0

0
0

2
0

0
0

80% immunization at age 5

time (years)

n
u

m
b

e
r Susceptible

Infected
Recovered/Immune
vaccinated

The next plot shows the case when the vaccination rate is only 50%. Now, the vaccine fails to control the
disease. The size of the outbreaks is slightly reduced, but the effect is minimal.

13

0 50 100 150 200 250 300

0
5

0
0

1
0

0
0

2
0

0
0

50% immunization at age 5

time (years)

n
u

m
b

e
r Susceptible

Infected
Recovered/Immune
vaccinated

Herd Immunity

Look back at the first plot. Note that after vaccination has become common that the proportion of Susceptibles
and Recovered/Immune was approximately the same as before the epidemic (e.g.the number of susceptible
after the vaccine introduction is similar to the average across cycles prior to the introduction). The manner
in which people gain immunity changes: before vaccination they gained immunity through getting the disease.
After the vaccine, they gain immunity by being vaccinated. However, the numbers are similar.

The key point: Even though the number of susceptibles in the population is about the same
as pre-vaccine, the susceptibles mostly don’t catch the disease anymore. This is because the
incidence of the disease is much lower in the population. Even though people are susceptible,
they don’t get the disease because they don’t encounter infected people. This phenomenon is
known as herd immunity

Here is the definition if herd immunity from Wikipedia:

Herd immunity (also called herd effect, community immunity, population immunity, or social immunity)
is a form of indirect protection from infectious disease that occurs when a large percentage of a population
has become immune to an infection, thereby providing a measure of protection for individuals who are not
immune.In a population in which a large number of individuals are immune, chains of infection are likely
to be disrupted, which stops or slows the spread of disease. The greater the proportion of individuals in a
community who are immune, the smaller the probability that those who are not immune will come into contact
with an infectious individual.

Herd immunity is a key part of the benefit of vaccination programs. Because of this, parents choosing to not
vaccinate their children has impact beyond their own children. There are many people in the population
who cannot be vaccinated. This includes kids that are too young to receive the vaccine and people who with

14

compromised immune systems who are unable to be vaccinated. When vaccination rates are high in the
rest of the population, then these people are protected by herd immunity. However, when vaccination rates
decrease, then herd immunity is lessened and disease outbreaks can occur. We see in the simulations above
that the size of disease outbreaks was much higher for 80% vaccination rate than for 90%. That is, even if
only 10% of the population decide to not vaccinate their children then many more people will get the disease.
Typically, babies and young children are hardest hit because they are too young for vaccination.

Mathematical models have played a large role in epidemiology and particularly in the area of vaccination
policy. As we have seen the dynamics are complicated and often non-intuitive. The use of models allows
us to explore the ramifications of different vaccination strategies without having to try them out in a real
population.

Eradicating Diseases

In order to eradicate a disease. the reproductive rate must be reduced to less than one. Suppose that before
the vaccination campaign, that the equilibrium number of susceptibles is S∗. Then, the disease effective
intrinsic reproductive rate is

Re =
S∗β

γ + µ

If the vaccination rate is v, then the number of susceptibles is reduced by the proportion v and Re becomes

Re =
(1 − p)S∗β
γ + µ

If Re is reduced below one after the vaccination campaign, then the disease will be eradicated.

Consider the disease simulated in the last three figures. Before the vaccination begins, there are outbreaks
when the number of susceptibles reaches about 1800.

The mean infection rate is about 0.05/365 (it varies by age, but is near 0.05 per year) and the recovery rate is
0.1 for all age groups. The background mortality rate is 0.015 except for individuals over 70. Thus, we have

Re =
S∗β

γ + µ

1800 ∗ 0.05/365
0.1 + 0.015

= 2.14

Children are vaccinated at 5 years old and are susceptible up until that point. The proportion of children
under 5 is about 15%:
sum(pop[,2]<5*365)/3000

## [1] 0.1473333

Thus, the total proportion of vaccinated people in the population is

proportion over 5 ∗ vaccination rate

With a 90% vaccination rate for 5-year olds, we have

Re = 2.14 ∗ (1 − 0.9 ∗ 0.85) = 0.5

With an 80% vaccination rate, we have

Re = 2.15 ∗ (1 − 0.8 ∗ 0.85) = 0.42

15

With an 50% vaccination rate, we have

Re = 2.15 ∗ (1 − 0.5 ∗ 0.85) = 1.23

Re is below one for 90% and 80% vaccination rates. In both of these cases, the disease was largely eliminated
except for small outbreaks coming from new input of infecteds. With a vaccination rate of 50%, Re > 1 and
we see that the disease persists in the population with major outbreaks continuing

When do epidemics end?

An epidemic ends when Re drops below one. That is, when infected people on average infect less than one
other person.

Recall this expression for Re:

Re =
S

N

γ + µ
=

γ + µ

Key points:

1. The effective disease reproductive rate Re is decreased when susceptibles become a lower proportion of
the population.

2. The proportion of people who are susceptible drops by people becoming immune.

3. People become immune either by getting the disease or by being vaccinated.

The epidemic ends when the number of people who become immune by getting the disease
plus the number of people who become immune by being vaccinated becomes large enough
that infected people will not encounter large numbers of susceptible people.

The exact percentage of immune people that is required depends on the details of the disease.

Another key point:

If there is not vaccination (and nothing else changes) then there are likely to be further
outbreaks. This is because there will be an inflow of new susceptibles by birth. If they are
not vaccinated, then the number of susceptibles will eventually become high enough to fuel a
new outbreak. Alternatively, the disease will become endemic: always in the population at a
steady low level.

If we don’t want this, then

GET VACCINATED

Age at Infection

The impacts of vaccination are heavily impacted by the age at which infections typically occur. In order to
be effective, the vaccine has to be administered at an earlier age than most people will get the disease. With
many of the historically deadly diseases (e.g. measles), people would most often catch them in childhood.
This is not necessarily because children are more susceptible. If infection rates are high, then most people
will catch it within a few years of exposure. For example, suppose that the probability of infection is 20% per
year for people of all ages. Then most kids will catch the disease before they are five – not because they are
more vulnerable than anyone else to infection, but because it is not possible last longer than a few years
without catching it. For a disease with lower infection rates, the average age of infection can be much older.

16

Consider the plot below. I set the infection rate to 5% per year for all ages and the recory rate is 10% per
day. The bottom plot shows the average age at infection over the population. We see that it varies between
10 and 18 years of age as the intensity of the epidemic varies. When the number of susceptibles is high, then
children are catching the disease around 10-12 years old. After an outbreak when the number of suscepibles
is low, the average age of infection increases to 16-18. In all cases, it is predominant children who catch the
disease, even though the probability of disease transmission is the same for all ages. This is because older
people predominantly already caught the disease when they were young and thus are immune.

200 250 300 350 400 450 500

0
1

5
0

0

disease dynamics, beta=0.05/365 for all ages

time (years)

n
u

m
b

e
r

200 250 300 350 400 450 500

1
0

1
4

1
8

Average Age at Infection

a
ve

ra
g

e
a

g
e

(
ye

a
rs

)

Vaccination and Age of Infection

Now, let’s consider what happens when we introduce vaccination:

The first plot below has vaccination at age 5. In this case, the average age at infection drops after the
vaccination campaign begins. This is because most infections happen in children who are not vaccinated yet.

17

200 300 400 500 600

0
1

5
0

0
vaccinated at age 5

time (years)

n
u

m
b

e
r

200 300 400 500 600

0
1

5
3

0

Average Age at Infection

a
ve

ra
g

e
a

g
e

(
ye

a
rs

)

In the next simulation, children are vaccianted at birth. Before the vaccination campaign, the average age
of infection is around six. After the vaccination campaign, the average age of infection increases to the
range 14-18. This happens because of herd immunity. Because there are many fewer infected people in the
population than before the vaccination, those who are not vaccinated encounter many fewer infected people.
Thus, they are typically teenagers when they get the disease.

18

200 300 400 500 600

0
1

5
0

0
vaccinated at birth

time (years)

n
u

m
b

e
r

200 300 400 500 600

6
1

2
1

8

Average Age at Infection

a
ve

ra
g

e
a

g
e

(
ye

a
rs

)

Vaccines can strongly impact the age at which people tend to get the disease and frequently
will increase the average age at which someone gets the disease

Is this necessarily a good thing? Consider the case of rubella:

Case Study: Rubella

From Wikipedia:

Rubella, also known as German measles or three-day measles, is an infection caused by the rubella virus
This disease is often mild with half of people not realizing that they are infected. A rash may start around
two weeks after exposure and last for three days. It usually starts on the face and spreads to the rest of the
body.The rash is sometimes itchy and is not as bright as that of measles.Swollen lymph nodes are common
and may last a few weeks. A fever, sore throat, and fatigue may also occur. In adults joint pain is common.
Complications may include bleeding problems, testicular swelling, and inflammation of nerves. Infection
during early pregnancy may result in a child born with congenital rubella syndrome (CRS) or miscarriage.
Symptoms of CRS include problems with the eyes such as cataracts, ears such as deafness, heart, and brain.
Problems are rare after the 20th week of pregnancy. Rubella is usually spread through the air via coughs of
people who are infected.People are infectious during the week before and after the appearance of the rash.
Babies with CRS may spread the virus for more than a year.[1] Only humans are infected. Insects do not
spread the disease. Once recovered, people are immune to future infections. Testing is available that can
verify immunity. Diagnosis is confirmed by finding the virus in the blood, throat, or urine. Testing the blood
for antibodies may also be useful.[1] Rubella is preventable with the rubella vaccine with a single dose being
more than 95Rubella is a common infection in many areas of the world. Each year about 100,000 cases of
congenital rubella syndrome occur. Rates of disease have decreased in many areas as a result of vaccination.
There are ongoing efforts to eliminate the disease globally. In April 2015 the World Health Organization

19

declared the Americas free of rubella transmission. The name “rubella” is from Latin and means little red.
It was first described as a separate disease by German physicians in 1814 resulting in the name “German
measles.”

Children in the US receive the MMR (measles-mumps-rubella) vaccine. The first dose is at around one year
old and the second dose is in the range 4-6 years old.

A key characteristic of rubella is that it is usually mild, except when pregnant mothers transmit it to their
babies in early pregnancy. The resulting congenital rubella syndrome can be devastating in the newborn
baby. Thus, the most important goal in controlling rubella is preventing women of child-bearing age from
becoming infected.

Rubella vaccine camapigns commenced in the 1970’s. In a seminal 1983 paper, Anderson and May (Vaccination
against rubella and measles: quantitative investigations of different policies) explored the implications of
different vaccination policies for rubella.

In the US, the initial rubella vaccination campaign took the strategy of vaccinating all children 15 months or
older. The trend over time in cases of rubella and CRS are shown in Figure 4. We see that the number of

Statistics homework help

Data and Questions

MAG DEPTH
0.75 7.5
0.74 2.5
0.64 14.0
1.20 15.5
0.70 3.0
2.20 2.4
1.98 14.4
0.64 5.7
1.22 6.1
0.50 7.1
1.64 17.2
1.32 8.7
3.87 9.3
0.90 12.3
1.76 9.8
1.00 7.4
1.26 17.1
0.01 8.8
0.65 5.0
1.46 19.1
1.62 12.7
1.83 4.7
0.99 6.8
1.56 6.0
0.40 14.6
1.28 4.9 r
0.83 19.1 CV
1.34 9.9
0.54 16.1
1.25 4.6
0.92 4.9
1.25 16.3
0.79 14.0 Slope
0.79 4.2 Y-intercept
1.44 5.4 Regression Equation
1.00 5.9
2.24 15.6
2.50 7.7
1.79 16.4
1.25 15.4
1.49 4.9
0.84 8.1 y-hat
1.42 7.5 y-bar
1.00 14.1
1.25 11.1
1.42 14.8
1.35 4.6
1.45 7.1
0.40 3.1
1.39 5.3

Slide 3. Construct a Scatterplot Below.

Slide 4. Find the value of the linear correlation coefficient r and the critical value of r using α = 0.05. Include an explanation on how you found those values.

Slide 6. Find the regression equation. Let the predictor (x) variable be the magnitude. Identify the slope and the y-intercept within your regression equation.

Slide 7. Is the equation a good model? Explain. What would be the best predicted depth of an earthquake with a magnitude of 2.0? Include the correct units.
*Hint: You only need to find y-hat or y-bar (not both).

*Note: Refer to the deliverable instructions for a breakdown of the PowerPoint requirements.

Statistics homework help

Q1. What is a Markov Chain? Provide an example, including digraph with transition probabilities.

Q2. How is a Hidden Markov Model different from a Markov Chain? How is it similar?

Q3. What is Bayes’ Theorem? Why is it controversial?

Q4. What is GWAS? How does it work? Be specific!

Q5. What is a SNP? How can they be used to identify disease-causing genes? Are SNPs the causative agent of diseases? Why or why not?

Statistics homework help

The mean body mass index (BMI) for boys of age 12 years is 23.6. An investigator wants to test if the BMI is higher in 12 years old boys living in New York City. How many boys are needed to ensure that a two sided test of hypothesis has 80% power to detect a difference in BMI of 2 units? Assume that the standard deviation in BMI is 5.7.

Statistics homework help

Data

Job Title Salary
Accountants and Auditors 65120 source: http://www.bls.gov/
Actuaries 99120
Administrative Law Judges, Adjudicators, and Hearing Officers 142840 Calculations/Values Formulas/Answers
Administrative Services Managers 97180 Mean
Adult Basic and Secondary Education and Literacy Teachers and Instructors 63940 Standard Deviation
Advertising and Promotions Managers 105130 n
Advertising Sales Agents 51740
Aerospace Engineering and Operations Technicians 57140
Aerospace Engineers 115220
Agents and Business Managers of Artists, Performers, and Athletes 74580
Agricultural and Food Science Technicians 40060
Agricultural Inspectors 54140
Agricultural Sciences Teachers, Postsecondary 87390
Air Traffic Controllers 114906
Aircraft Cargo Handling Supervisors 50380
Aircraft Structure, Surfaces, Rigging, and Systems Assemblers 51410
Airfield Operations Specialists 59800
Airline Pilots, Copilots, and Flight Engineers 115670
Anthropologists and Archeologists 51720
Appraisers and Assessors of Real Estate 52870
Arbitrators, Mediators, and Conciliators 86430
Architects, Except Landscape and Naval 81000
Architectural and Civil Drafters 62210
Architecture and Engineering Occupations 73850
Architecture Teachers, Postsecondary 73870
Archivists 76749
Art Directors 98924
Art, Drama, and Music Teachers, Postsecondary 78700
Athletic Trainers 45440
Atmospheric and Space Scientists 93900
Atmospheric, Earth, Marine, and Space Sciences Teachers, Postsecondary 96590
Audiologists 97230
Avionics Technicians 47320
Biomedical Engineers 99000
Boilermakers 76310
Broadcast News Analysts 71040
Brokerage Clerks 57260
Budget Analysts 75940
Business and Financial Operations Occupations 64880
Business Operations Specialists, All Other 67980
Business Teachers, Postsecondary 109800
Buyers and Purchasing Agents, Farm Products 62290
Camera and Photographic Equipment Repairers 32280
Captains, Mates, and Pilots of Water Vessels 63890
Cardiovascular Technologists and Technicians 59630
Career/Technical Education Teachers, Middle School 69050
Career/Technical Education Teachers, Secondary School 63430
Cargo and Freight Agents 40910
Cartographers and Photogrammetrists 72120
Chefs and Head Cooks 47660
Chemical Engineers 87200
Chemical Equipment Operators and Tenders 45460
Chemical Plant and System Operators 54920
Chemical Technicians 50360
Chemistry Teachers, Postsecondary 96330
Chemists 59630
Child, Family, and School Social Workers 58140
Chiropractors 86820
Civil Engineers 91430
Claims Adjusters, Examiners, and Investigators 66030
Clinical, Counseling, and School Psychologists 76150
Coil Winders, Tapers, and Finishers 36610
Commercial and Industrial Designers 66710
Commercial Pilots 130059
Communications Equipment Operators, All Other 43160
Communications Teachers, Postsecondary 85310
Community and Social Service Occupations 43790
Community Health Workers 37190
Compensation and Benefits Managers 121570
Compensation, Benefits, and Job Analysis Specialists 67210
Compliance Officers 67637
Computer and Information Research Scientists 121310
Computer and Information Systems Managers 137140
Computer and Mathematical Occupations 81640
Computer Hardware Engineers 95500
Computer Network Architects 112050
Computer Network Support Specialists 70940
Computer Occupations, All Other 92960
Computer Programmers 84280
Computer Science Teachers, Postsecondary 89290
Computer Systems Analysts 90600
Computer User Support Specialists 53680
Conservation Scientists 67540
Construction and Building Inspectors 64150
Construction Managers 99150
Continuous Mining Machine Operators 55330
Control and Valve Installers and Repairers, Except Mechanical Door 64960
Conveyor Operators and Tenders 35110
Cost Estimators 69480
Crane and Tower Operators 53980
Credit Analysts 72870
Credit Counselors 46720
Criminal Justice and Law Enforcement Teachers, Postsecondary 66980
Curators 66230
Database Administrators 91730
Dental Hygienists 71930
Derrick Operators, Oil and Gas 38120
Detectives and Criminal Investigators 90890
Diagnostic Medical Sonographers 74340
Dietitians and Nutritionists 60370
Directors, Religious Activities and Education 43690
Drafters, All Other 51790
Economics Teachers, Postsecondary 137920
Economists 106280
Editors 58820
Education Administrators, All Other 79960
Education Administrators, Elementary and Secondary School 103570
Education Administrators, Postsecondary 110110
Education Administrators, Preschool and Childcare Center/Program 81590
Education Teachers, Postsecondary 65020
Education, Training, and Library Occupations 47920
Educational, Guidance, School, and Vocational Counselors 56550
Electric Motor, Power Tool, and Related Repairers 63800
Electrical and Electronics Drafters 69010
Electrical and Electronics Engineering Technicians 68060
Electrical and Electronics Installers and Repairers, Transportation Equipment 54060
Electrical and Electronics Repairers, Commercial and Industrial Equipment 55970
Electrical and Electronics Repairers, Powerhouse, Substation, and Relay 81590
Electrical Engineers 91870
Electrical Power-Line Installers and Repairers 67430
Electricians 60590
Electro-Mechanical Technicians 54700
Electronics Engineers, Except Computer 100610
Elementary School Teachers, Except Special Education 62620
Elevator Installers and Repairers 88340
Embalmers 48770
Emergency Management Directors 79270
Engineering Technicians, Except Drafters, All Other 63250
English Language and Literature Teachers, Postsecondary 81700
Environmental Engineering Technicians 56810
Environmental Engineers 84870
Environmental Science and Protection Technicians, Including Health 45090
Environmental Science Teachers, Postsecondary 92530
Environmental Scientists and Specialists, Including Health 84320
Epidemiologists 85620
Executive Secretaries and Executive Administrative Assistants 55770
Exercise Physiologists 54300
Explosives Workers, Ordnance Handling Experts, and Blasters 62910
Extruding, Forming, Pressing, and Compacting Machine Setters, Operators, and Tenders 38680
Farm and Home Management Advisors 38940
Film and Video Editors 62280
Financial Analysts 85660
Financial Clerks, All Other 44080
Financial Examiners 101500
Financial Managers 134370
Financial Specialists, All Other 87690
Fire Inspectors and Investigators 58590
Firefighters 49620
First-Line Supervisors of Construction Trades and Extraction Workers 82160
First-Line Supervisors of Correctional Officers 84290
First-Line Supervisors of Farming, Fishing, and Forestry Workers 43150
First-Line Supervisors of Fire Fighting and Prevention Workers 91930
First-Line Supervisors of Helpers, Laborers, and Material Movers, Hand 49590
First-Line Supervisors of Landscaping, Lawn Service, and Groundskeeping Workers 54280
First-Line Supervisors of Mechanics, Installers, and Repairers 66430
First-Line Supervisors of Non-Retail Sales Workers 72920
First-Line Supervisors of Office and Administrative Support Workers 58120
First-Line Supervisors of Police and Detectives 101240
First-Line Supervisors of Production and Operating Workers 60990
First-Line Supervisors of Protective Service Workers, All Other 46280
First-Line Supervisors of Transportation and Material-Moving Machine and Vehicle Operators 58250
Fish and Game Wardens 75430
Food Service Managers 51340
Foreign Language and Literature Teachers, Postsecondary 73350
Forensic Science Technicians 79630
Forest and Conservation Technicians 46640
Foresters 65970
Forestry and Conservation Science Teachers, Postsecondary 90080
Fundraisers 57720
Funeral Service Managers 82590
Gaming Supervisors 32220
Gas Compressor and Gas Pumping Station Operators 62720
Gas Plant Operators 70130
General and Operations Managers 124190
Geography Teachers, Postsecondary 82530
Geological and Petroleum Technicians 39180
Geoscientists, Except Hydrologists and Geographers 70730
Health and Safety Engineers, Except Mining Safety Engineers and Inspectors 84880
Health Diagnosing and Treating Practitioners, All Other 67650
Health Educators 41781
Health Specialties Teachers, Postsecondary 136670
Health Technologists and Technicians, All Other 45940
Healthcare Practitioners and Technical Occupations 67470
Healthcare Social Workers 53600
Hearing Aid Specialists 46970
Historians 84337
History Teachers, Postsecondary 88590
Hoist and Winch Operators 80,660
Home Economics Teachers, Postsecondary 74490
Human Resources Managers 112430
Human Resources Specialists 61460
Industrial Engineering Technicians 55460
Industrial Engineers 82720
Industrial Machinery Mechanics 55930
Industrial Production Managers 100480
Information and Record Clerks, All Other 45700
Information Security Analysts 97360
Installation, Maintenance, and Repair Occupations 45990
Instructional Coordinators 66810
Insurance Appraisers, Auto Damage 70380
Insurance Sales Agents 66080
Insurance Underwriters 76990
Interior Designers 62010
Judges, Magistrate Judges, and Magistrates 58140
Kindergarten Teachers, Except Special Education 55850
Labor Relations Specialists 51870
Landscape Architects 68960
Lawyers 140920
Layout Workers, Metal and Plastic 42830
Legal Occupations 82900
Legal Support Workers, All Other 60100
Librarians 56320
Library Science Teachers, Postsecondary 78830
Life Scientists, All Other 82630
Life, Physical, and Social Science Occupations 62840
Loading Machine Operators, Underground Mining 41270
Loan Officers 63040
Locomotive Engineers 71960
Logging Workers, All Other 41940
Logisticians 74600
Magnetic Resonance Imaging Technologists 70580
Management Analysts 92200
Managers, All Other 88600
Marine Engineers and Naval Architects 82410
Market Research Analysts and Marketing Specialists 62380
Marketing Managers 122260
Marriage and Family Therapists 55600
Materials Engineers 91510
Mathematical Science Teachers, Postsecondary 78880
Mechanical Drafters 58540
Mechanical Engineering Technicians 60220
Mechanical Engineers 92040
Media and Communication Equipment Workers, All Other 76540
Medical and Clinical Laboratory Technologists 65770
Medical and Health Services Managers 113030
Medical Equipment Repairers 58310
Meeting, Convention, and Event Planners 52370
Mental Health Counselors 46580
Metal-Refining Furnace Operators and Tenders 44990
Middle School Teachers, Except Special and Career/Technical Education 66630
Millwrights 57190
Mine Cutting and Channeling Machine Operators 46250
Mine Shuttle Car Operators 56930
Mining and Geological Engineers, Including Mining Safety Engineers 93920
Mining Machine Operators, All Other 69160
Mixing and Blending Machine Setters, Operators, and Tenders 41970
Mobile Heavy Equipment Mechanics, Except Engines 58950
Model Makers, Metal and Plastic 57100
Morticians, Undertakers, and Funeral Directors 69800
Multimedia Artists and Animators 59890
Music Directors and Composers 46260
Natural Sciences Managers 113620
Network and Computer Systems Administrators 87700
Nuclear Engineers 121650
Nuclear Medicine Technologists 79440
Nuclear Technicians 88770
Nurse Practitioners 101960
Nursing Instructors and Teachers, Postsecondary 72450
Occupational Health and Safety Specialists 75610
Occupational Health and Safety Technicians 61740
Occupational Therapists 82290
Occupational Therapy Assistants 61860
Operations Research Analysts 90310
Optometrists 111790
Orthotists and Prosthetists 82380
Painters, Transportation Equipment 45230
Paper Goods Machine Setters, Operators, and Tenders 37110
Paralegals and Legal Assistants 56990
Patternmakers, Metal and Plastic 56260
Personal Financial Advisors 121750
Petroleum Pump System Operators, Refinery Operators, and Gaugers 66550
Pharmacists 120280
Philosophy and Religion Teachers, Postsecondary 78010
Physical Therapist Assistants 58720
Physical Therapists 90040
Physician Assistants 104730
Physicists 118520
Physics Teachers, Postsecondary 89040
Plant and System Operators, All Other 56830
Plumbers, Pipefitters, and Steamfitters 77570
Podiatrists 194130
Police and Sheriff’s Patrol Officers 73870
Political Science Teachers, Postsecondary 90250
Postal Service Clerks 49310
Postal Service Mail Carriers 50160
Postal Service Mail Sorters, Processors, and Processing Machine Operators 49820
Postmasters and Mail Superintendents 75620
Power Distributors and Dispatchers 84830
Power Plant Operators 79100
Precision Instrument and Equipment Repairers, All Other 64170
Private Detectives and Investigators 58290
Probation Officers and Correctional Treatment Specialists 64300
Producers and Directors 75970
Production, Planning, and Expediting Clerks 48390
Property, Real Estate, and Community Association Managers 66710
Psychologists, All Other 79010
Psychology Teachers, Postsecondary 89680
Public Relations and Fundraising Managers 115180
Public Relations Specialists 63620
Pump Operators, Except Wellhead Pumpers 51520
Purchasing Agents, Except Wholesale, Retail, and Farm Products 61760
Purchasing Managers 111380
Radiation Therapists 84640
Radio, Cellular, and Tower Equipment Installers and Repairers 49240
Radiologic Technologists 63420
Rail Yard Engineers, Dinkey Operators, and Hostlers 54790
Railroad Conductors and Yardmasters 65740
Rail-Track Laying and Maintenance Equipment Operators 54600
Real Estate Brokers 88750
Real Estate Sales Agents 59010
Recreation and Fitness Studies Teachers, Postsecondary 60080
Recreational Vehicle Service Technicians 34450
Refractory Materials Repairers, Except Brickmasons 49210
Registered Nurses 71730
Reinforcing Iron and Rebar Workers 86290
Respiratory Therapists 56910
Rolling Machine Setters, Operators, and Tenders, Metal and Plastic 38060
Roof Bolters, Mining 58900
Rotary Drill Operators, Oil and Gas 49720
Sales Engineers 98760
Sales Managers 75432
Sales Representatives, Services, All Other 61930
Sales Representatives, Wholesale and Manufacturing, Except Technical and Scientific Products 69900
Sales Representatives, Wholesale and Manufacturing, Technical and Scientific Products 81950
Secondary School Teachers, Except Special and Career/Technical Education 68380
Securities, Commodities, and Financial Services Sales Agents 86070
Service Unit Operators, Oil, Gas, and Mining 42200
Set and Exhibit Designers 54620
Ship Engineers 57066
Signal and Track Switch Repairers 38120
Social and Community Service Managers 63870
Social Scientists and Related Workers, All Other 79960
Social Work Teachers, Postsecondary 54580
Social Workers, All Other 65890
Sociology Teachers, Postsecondary 87710
Software Developers, Applications 96110
Software Developers, Systems Software 106700
Soil and Plant Scientists 57080
Sound Engineering Technicians 58660
Special Education Teachers, All Other 59400
Special Education Teachers, Kindergarten and Elementary School 65430
Special Education Teachers, Middle School 62160
Special Education Teachers, Secondary School 68560
Speech-Language Pathologists 78760
Stationary Engineers and Boiler Operators 79090
Statisticians 88190
Surveyors 60215
Tank Car, Truck, and Ship Loaders 45470
Tax Examiners and Collectors, and Revenue Agents 79850
Technical Writers 67410
Telecommunications Equipment Installers and Repairers, Except Line Installers 57580
Tire Builders 42500
Tool and Die Makers 54680
Training and Development Managers 101500
Training and Development Specialists 59910
Transportation Inspectors 86790
Transportation, Storage, and Distribution Managers 93250
Urban and Regional Planners 79510
Veterinarians 93830
Water and Wastewater Treatment Plant and System Operators 54560
Web Developers 57450
Wholesale and Retail Buyers, Except Farm Products 55080
Writers and Authors 53050
Zoologists and Wildlife Biologists 62420

Question 1

1. Describe the 8 steps in the process for hypothesis testing. Include an explanation of the decision criteria for rejecting the null hypothesis for both the p-value method and the critical value method.

Question 2

Calculations/Values Formulas/Answers
Mean (x-bar)
Standard Deviation
n
mu
Test Statistic
Critical Value
P-value

2a. Write the null and alternative hypotheses symbolically and identify which hypothesis is the claim. Then identify if the test is left-tailed, right-tailed, or two-tailed and explain why.

2b. Identify and explain which test statistic you will use for your hypothesis test: z or t? Find the value of the test statistic.

Provide your calculations in the cells designated to the right. Explain your answers below.

2c. What is the critical value? Describe the rejection region of this hypothesis test.

Provide your calculations in the cells designated to the right. Explain your answers below.

2d. Using the critical value approach, should you reject the null hypothesis or not reject the null hypothesis? Explain. After making your decision, restate it in non-technical terms and make a conclusion about the original claim.

2e. Calculate the p-value for this hypothesis test, and state the hypothesis conclusion based on the p-value. Does this match your results from the critical value method?

Provide your calculations in the cells designated to the right. Explain your answers below.

Question 3

Calculations/Values Formulas/Answers
Mean (x-bar)
Standard Deviation
n
mu
Test Statistic
Critical Value
P-value

3a. Write the null and alternative hypotheses symbolically and identify which hypothesis is the claim. Then identify if the test is left-tailed, right-tailed, or two-tailed and explain why.

3b. Identify and explain which test statistic you will use for your hypothesis test: z or t? Find the value of the test statistic.

Provide your calculations in the cells designated to the right. Explain your answers below.

3c. What is the critical value? Describe the rejection region of this hypothesis test.

Provide your calculations in the cells designated to the right. Explain your answers below.

3d. Using the critical value approach, should you reject the null hypothesis or not reject the null hypothesis? Explain. After making your decision, restate it in non-technical terms and make a conclusion about the original claim.

3e. Calculate the p-value for this hypothesis test, and state the hypothesis conclusion based on the p-value. Does this match your results from the critical value method?

Provide your calculations in the cells designated to the right. Explain your answers below.