Work and life balance | Statistics homework help


For this assignment, we will be working to understand the impact of different working models on the perceived satisfaction of employees with regard to their work/life balance. Corporate goals often incentivize working longer hours and in more demanding roles. However, alternative models exist. Some businesses and countries are experimenting with shorter working weeks or changes to their corporate cultures.


To further examine the issue, a team of researchers partnered with a number of companies to examine the impact of their corporate culture and the length of the working week on the overall satisfaction of employees with regard to their work/life balance. In the first phase of the study, the researchers conducted an assessment of each company’s culture by interviewing a number of employees about the responsibilities, challenges, and stress related to their work. The corporate culture was then rated as either relaxed or demanding by the researchers based upon a review of this information across all of the participating employees in the company.

The second stage of the study included an experiment with working weeks of different lengths. Prior to the experiment, all of these companies operated with conventional 5-day working weeks and standard hours. Each company was randomized to implement either a 3-day working week, a 4-day working week, or to maintain its conventional 5-day working week. The overall number of expected working hours was held in proportion to the working week (e.g. 8 hours per day for the number of days worked). Training was provided to the managers and the employees to set reasonable expectations for what should be accomplished in the shortened working weeks. The companies were monitored to ensure compliance with the schedule and the expectations. The study was conducted over a period of 6 weeks.

At the end of this period, consenting employees were given a survey that assessed their satisfaction with their balance of work and life. The answers were combined into an overall measure of satisfaction ranging from 0 to 100.

In this assignment, we will be working with the information provided to analyze the satisfaction scores and consider other possible implications of changes in the typical working conditions of companies.


The data are available in the file work and life balance.csvPreview the document.

For each consenting employee, information on their years of experience and whether they are a manager was collected. Data about each employee’s company was recorded, including its identifier, industry, and the assessment of its working culture. The company’s randomly assigned workweek was included, and each employee’s overall satisfaction score was recorded.


Based upon the information above and the data provided, please answer the following questions. When numeric answers are requested, a few sentences of explanation should also be provided. Please show your code for any calculations performed.



You will be assessed on the accuracy and thoughtfulness of your responses.

  • Questions 1-20: 5 points apiece


  1. What are the primary research questions of the study? State them clearly in plain language. Then briefly explain the importance of this investigation.
  2. For each research question you mentioned above, describe how well the study is designed to evaluate the question.
  3. What kind of statistical method could be employed to analyze the data and evaluate the research questions?
  4. Fit your intended model and show a summary of its results. While you may include other variables, we will specifically exclude the company from the analysis because these effects would not generalize as well to the broader industries.
  5. Explain the results of your model. Describe how the estimates relate to your research questions and any other notable findings.
  6. Would variable interactions also play a role? If your research question includes multiple independent variables, then include pairwise interactions with them. If you think there is only one independent variable in the study, then create an interaction between that variable and other measured factors that you might consider relevant. Show the numeric results and comment on the interactions.
  7. Are there other variables that would be helpful to measure? Is this even necessary? Explain your answer and reasoning.
  8. What if we wanted to compare all of the average satisfaction scores in the three groups of working weeks? For this analysis, you may ignore the other variables. Show the results of a statistical test to simultaneously evaluate the difference in satisfaction for all of the pairs of possible working weeks. Comment on the results.
  9. Now conduct separate tests of whether a shorter working schedule increases satisfaction for each pair of schedules. Which of these results would remain significant with a Bonferroni correction for multiple comparisons? Show the p-values for the t-tests, the corrected threshold for a 0.05 significance level, and whether the differences remain significant after the adjustment.
  10. Do you think the 6 week time frame is an appropriate length to investigate the effect of changes in the working schedule on the satisfaction of work/life balance? Explain why or why not.
  11. Now the researchers would like to build upon the work of the first experiment they conducted. In the comments on the surveys, a sizable number of the employees in the first study noted that they did not get enough sleep with a 5-day working week. Anecdotally, those working the shorter weeks during the experiment frequently mentioned the benefit of getting enough rest.
    With this in mind, the researchers would like your help in planning their next experiment. They would once again like to randomize companies to shorter working weeks. Based on the feedback of the previous experiment, a 3-day working week would not be very practical for the companies, while 4 days seemed more actionable. Comparing the amount of sleep of employees with 4-day schedules to the amount of sleep of those with 5-day schedules, how would you conduct the experiment to answer this question? State a research question, comment on the operational designs, and describe the type of data you would gather.
  12. What kind of statistical test would be appropriate for your research question? Provide sufficient details on all of the choices you would make.
  13. What kind of improvement in nightly sleeping times would you consider meaningful for the average employee? Explain your reasoning.
  14. The researchers are hoping to sample approximately 200 employees for the study, roughly divided into two groups of 100. What would be the power of your proposed statistical test in this scenario? Use your suggested effect size from the previous question in units of hours and a significance level of 0.05. For now, assume that the standard error of mean sleeping times is 1 hour. Produce a numeric answer and then comment on the results.
  15. It may be difficult to convince companies to consider a 4-day working week and to convince employees to provide you with their records of sleep. How would these results change if you could only get 30 employees in the 4-day working week? Assume that the other inputs from the previous question will be used. Calculate the power and comment on the results, along with the differences from the previous question.
  16. Assuming that we hold the other inputs fixed from the previous 2 questions, what sample size would be needed in the 4-day working week group to achieve a power of 0.9? Make sure to round your answer up to a whole number.
  17. Describe the trade-offs between power and sample size in this setting. Including considerations of the statistical issues along with the practical aspects of running the experiment.
  18. In our earlier analyses, we had assumed that the standard error of mean sleeping times was 1 hour. What if this assumption is incorrect? For now, you may consider an experiment with 100 sampled employees in each treatment group and a significance level of 0.05. Describe how the power changes if our assumption is wrong in each direction.
  19. The original experiment studied 3 different levels of working weeks (3, 4, and 5 days per week) and 2 levels of corporate culture (relaxed and demanding). Suppose we could randomize 100 employees into each combination of a working week and a corporate culture. We would like to study the differences in mean nightly sleeping time across these groups using a two-way ANOVA model while planning for a power of 0.8 using a significance level of 0.05. Under these circumstances, what kind of effect size could be detected? Convert the calculated effect size into minutes under an assumption that the standard error is 1 hour.
  20. Taking into account your analyses and statistical planning, what kind of recommendations would you make to the companies in order to help them to improve the satisfaction of their employees with regard to work/life balance?


Please turn in the following files:

  • Output file showing your code, answers, and explanations (.html file).
  • Source code (.Rmd file)

Please do not compress or zip these files.

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