General instructions

• You need to answer Questions 1 to 4 and then write a report that summarises and explains your

results from Questions 1 to 4.

• In each question, you will need to decide on the most appropriate hypothesis test to perform or a

statistical technique to apply.

• You will first need to download the data file SleepStudy2020.xlsx from the Data tab in learnonline

and decide which variables are categorical and which are numerical. Variable descriptions are given

in Appendix A, Table A.1. The decision tree from Week 7 called ‘Which statistical test?’ will also help.

Question 1 (20 marks)

Are you a Lark or an Owl? Studies indicate that about 10% of us are morning people (Larks) while 20%

are evening people (Owls) and the rest are neither. Studies also indicate that this circadian (owl/lark)

preference may not be settled until the age of 22 or later. In this question you are going to analyse

circadian preferences among university students.

(a) (10 marks) Is there evidence that the circadian (owl/lark) preferences for university students differ

from the claimed proportions? Formulate and perform an appropriate hypothesis test at a 5%

significance level using the summarised data shown in Table 1. Use the STATE-FORMULATE-SOLVECONCLUDE procedure and perform follow-up analysis if appropriate. For full marks, include

appropriate Minitab output.

Type Count Claimed proportion

Lark 41 0.1

Neither 163 0.7

Owl 49 0.2

Table 1. Circadian preference: Summary of survey responses and claimed proportions

Additional Minitab instructions: In order to complete this question, enter the data from Table 1

above into Minitab and perform a ‘Chi-Square Goodness-of-Fit (One Variable)’ test using the option

to ‘Test specific proportions’.

(b) (10 marks) How much do Larks and Owls differ in their sleep habits? Use Minitab to obtain the

confidence intervals for a comparison between Larks and Owls (ignore the Neither category) on

each of the variables WeekdayBed, WeekdayRise and WeekdaySleep. These variables are stored in

the SleepStudy2020.xlsx data file and their descriptions can be found in Table A.1 in Appendix A.

For full marks, include appropriate Minitab output and check the requirements. Do not use the full

STATE-FORMULATE-SOLVE-CONCLUDE procedure. Instead, identify and interpret confidence

intervals that correspond to statistically significant differences between Larks and Owls.

Additional Minitab instructions: In order to complete this question, unstack the columns

WeekdayBed, WeekdayRise and WeekdaySleep using categories in variable LarkOwl.

Question 2 (18 marks)

Does circadian preference matter when it comes to sleep quality? In order to address this question,

you are going to work with variables PoorSleepQuality and LarkOwl from the SleepStudy2020.xlsx data

file. Variables descriptions are given in Appendix A, Table A.1.

(a) (6 marks) Use Minitab to produce boxplots of PoorSleepQuality by circadian preference (three

categories in variable LarkOwl)shown horizontally within the same graph. Comment briefly on how

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sleep quality compares across circadian preference categories (Owl, Lark, Neither) and whether

you expect to find any statistically significant differences.

(b) (10 marks) Is there a statistically significant difference in sleep quality based on students’ circadian

preferences? Formulate and perform an appropriate hypothesis test at a 5% significance level. Use

the STATE-FORMULATE-SOLVE-CONCLUDE procedure. For full marks, include appropriate Minitab

output.

(c) (2 marks) Is it appropriate to argue cause and effect, in either direction, based on these results?

Why or why not? Explain briefly. Hint: What type of study is this?

Question 3 (10 marks)

Which sleep related habits might influence academic performance? In order to answer this question,

you are going to investigate the relationship between GPA and each of the following variables: time to

rise on weekdays, time to go to bed on weekdays, amount of sleep per night on weekdays, and the

number of missed classes. Answer the questions that follow.

(a) (4 marks) Use Minitab to obtain the Pearson correlation coefficient and the corresponding P-value

for GPA and each of the following variables: WeekdayRise, WeekdayBed, WeekdaySleep, and

ClassesMissed. Variable descriptions are given in Table A.1 in Appendix A. For full marks, include

relevant Minitab output here (i.e. four correlations and their P-values). Do not interpret that

output, you will do that in part (b).

(b) (6 marks) Based on your Minitab output in part (a), answer the following questions:

• Do sample correlations provide sufficient evidence of an association between GPA and the

other variables? In other words, which correlation estimates are statistically significant? How

do you know?

• How strong are the relationships that turned out to be statistically significant?

• Are your statistically significant correlations positive or negative? What does it mean in

practical terms for each relationship? Explain briefly.

Question 4 (24 marks)

Sleep Quality and DAS score. In the study students were rated on sleep quality (PoorSleepQuality) as

well as on Depression, Anxiety and Stress scales, with the DAS score (DASScore) giving a composite of

the three scores. How well does the DAS score predict sleep quality? Answer the questions that follow.

Variable descriptions are given in Table A.1 in Appendix A.

(a) (3 marks) Use Minitab to obtain a scatterplot with DASScore as the independent variable (x) and

PoorSleepQuality as the dependent variable (y). Does it make sense to fit a linear regression model

in this case? Justify your answer briefly.

(b) (2 marks) Use Minitab to fit a simple linear regression model including residual plots. You can

generate a fitted line plot if you wish (it is not required), but you must show regression tables from

the session window, together with residual plots. You will use the Minitab output from here to

answer questions that follow in parts (c) to (f).

(c) (6 marks) Are conditions for linear regression satisfied? Answer in terms of Linearity, Independence,

Normality and Population standard deviations.

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(d) (2 marks) Comment on the strength of the relationship between sleep quality and DAS score using

the coefficient of determination. What is its value? What precisely does it measure in this scenario?

(e) (2 marks) What is the value of the slope? What does it measure in this scenario?

(f) (3 marks) Is the relationship between sleep quality and DAS score statistically significant? In other

words, is the slope estimate statistically significant at 5% level? How do you know? Explain briefly.

(g) (6 marks) Suppose that one of the students at this university has a fairly high DAS score of 40. Use

Minitab to obtain a prediction of sleep quality for this student, including an appropriate interval for

that prediction. Discuss the accuracy of that prediction as shown in Week 9 workshop.

Statistical Analysis Report (28 marks)

Your report should consist of sections described below.

Introduction (3 marks)

Provide the context and rationale for the study. Use your own words!

There is no word limit, just ensure you have explained what the report will contain. As a guideline, one

paragraph is sufficient.

Methods (6 marks)

Discuss the methods used to collect and analyse data from this study:

• What type of study was conducted? Name the study design and briefly describe, in your own words,

the interventions that were part of this study.

• Describe the sample (including the sample size and any demographic information, e.g. who the

study participants were, their age, gender split etc).

• Briefly describe variables that you have analysed.

• Provide a list of statistical displays and procedures that you have used, along with confidence and

significance levels used in the analysis.

There is no word limit. As a guideline, one paragraph for this section is sufficient.

Results & Discussion (16 marks)

First, summarise the main results of your analyses from Questions 1 to 4. You may use subsections,

tables etc. as you see fit. Present and discuss results in a clear and simple way:

• Present findings of statistical analyses in a logical sequence. Descriptive statistics about variables

of interest are usually presented first, followed by the results of further statistical analyses.

• Include copies of key diagrams from Questions 1 to 4 as relevant to your presentation of results.

Useful diagrams to include in a report are bar charts, histograms, boxplots, error diagrams,

scatterplots, etc. Normal Probability Plots or residual plots should not be included in the report.

• State each result and the corresponding statistical procedure, and report P-values to three decimal

places. However, do not include numerical calculations or full details of statistical procedures and

condition checking (e.g. full Minitab output).

Next, interpret your statistical findings by discussing their practical significance. Use plain language;

there should be no technical details or statistical terminology. Are any of the results surprising?

Finally, in another short paragraph indicate shortcomings, if any, of the study design and analyses that

were performed. Are there any issues with internal and external validity of this study?

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There is no word limit. As a guideline, one and a half pages (two pages at most) will be sufficient for this

section, including any tables and graphs. Remember, marks are awarded for quality not quantity!

Conclusion (3 marks)

What can you conclude from your analysis about sleep quality, mood, circadian preference and

academic performance? Which factors appear to be important?

There is no word limit. As a guideline, one paragraph will be sufficient. Do not introduce any new

information in this section, and do not simply repeat statements made elsewhere in your report!

Note: You are not required to include additional sources (e.g. internet articles or scientific papers) but

if you do, ensure you include a reference list and cite them in text appropriately.

Appendix A. Data file and variable descriptions

Some of the data from the Onyper et al (2012) study is stored in the file called SleepStudy2020.xlsx that

can be downloaded from the Data tab within the course website. Below are descriptions of variables in

that data file:

Name Description

ClassesMissed Number of classes missed in a semester

ClassYear Year level from first to fourth year, coded 1 to 4

DASScore Combined score on Depression, Anxiety and Stress scale, commonly

used to assess mood. Higher values indicate more mood complaints,

e.g. depression, anxiety and/or stress

Gender 0 = Female and 1 = Male

GPA Grade point average measured on 0-4 scale, self-reported

LarkOwl Responses to the following survey question: ‘Are you an early riser or

a night owl?’ Possible categories: Lark, Neither, or Owl

PoorSleepQuality Measure of sleep quality derived from responses to the Pittsburgh

Sleep Quality Index (PSQI) questionnaire. Higher values indicate

poorer sleep

WeekdayBed Typical weekday bedtime derived from responses on PSQI and sleep

diaries, reported in hours since previous midnight, e.g. a bedtime of

25 corresponds to going to bed at 1:00am

WeekdayRise Typical weekday rise time derived from responses on PSQI and sleep

diaries, reported in hours since midnight, e.g. a rise time of 7.25

corresponds to getting up at 7:15 am

WeekdaySleep Typical weekday sleep duration, estimated as a period of time from

shutting the eyes with intent to go to sleep until the time the

participants awoke and did not close their eyes to go back to sleep.

Derived from responses on PSQI and sleep diaries and reported in

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