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## Statistics

Quantitative Methods in Health Statistical Analysis Report -

Question 1 -

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 not specifically classified as either. Studies also indicate that this circadian preference may not be settled until the age of 22 or later.

(a) Is there evidence that the owl/lark preferences for university students differ from the claimed proportions? Formulate and perform an appropriate hypothesis test at 5% significance level using the data shown in Table 2. Use Minitab to obtain the test statistic and the P-value. For full marks, include appropriate Minitab output. Use the STATE-FORMULATE-SOLVE-CONCLUDE procedure and perform follow-up analysis if appropriate.

 Type Count Claimed proportion Lark 41 0.1 Neither 163 0.7 Owl 49 0.2 Table - Circadian preference: Summary of survey responses and claimed proportions

Additional Minitab instructions: In order to complete this question, enter the data from Table above into Minitab and perform a 'Chi-Square Goodness-of-Fit (One Variable)' test using the option to 'Test specific proportions'.

(b) Are stress levels of students affected by circadian preference? Use Minitab to obtain a 100% stacked column chart that shows the conditional distribution of stress level given circadian preferences. Make two observations based on your chart.

(c) Test to see if there is a statistically significant relationship between the variables LarkOwl and Stress (see descriptions in Table 1- attached). Formulate and perform an appropriate hypothesis test at 5% significance level. Use Minitab to obtain the test statistic and the P-value. For full marks, include appropriate Minitab output. Use the STATE-FORMULATESOLVE-CONCLUDE procedure and perform follow-up analysis if appropriate.

Question 2 -

Are cognitive skills and alcohol use related? In order to address this question, you are going to work with variables CognitionZscore and AlcoholUse from the SleepStudy.xlsx data file. Descriptions of these variables are given in Table 1.

(a) Use Minitab to produce boxplots of cognitive scores by alcohol use shown horizontally within the same graph. Comment briefly on how cognitive scores compare across groups and whether you expect to find any statistically significant differences.

(b) Is there a significant difference in mean cognitive skills based on the level of alcohol use as reported by students? Formulate and perform an appropriate hypothesis test at 5% significance level. Use Minitab to obtain the test statistic and the P-value. For full marks, include appropriate Minitab output. Use the STATE-FORMULATE-SOLVECONCLUDE procedure.

(c) 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 -

Which attitudes and habits might influence academic performance? In order to answer this question, you are going to investigate the correlation between GPA and each of the following variables: the number of early classes, the number of missed classes and the average hours of sleep. Answer the questions that follow. Variable descriptions are shown in Table 1.

(a) Obtain the Pearson correlation coefficient and the corresponding P-value for GPA and the number of early classes (NumEarlyClass). What does a positive correlation mean in this case? Does the sample correlation provide sufficient evidence of an association between those two variables? Explain briefly.

(b) Now obtain the Pearson correlation coefficient and the corresponding P-value for GPA and the number of missed classes (ClassesMissed). Does the sample correlation provide sufficient evidence of an association between those two variables? Is it positive or negative? What does it mean in practical terms? Explain briefly.

(c) Finally obtain the Pearson correlation coefficient and the corresponding P-value for GPA and the average hours of sleep (AverageSleep). What does a positive correlation mean in this case? Does the sample correlation provide sufficient evidence of an association between those two variables? Explain briefly.

Question 4 -

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 1.

(a) 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) Use Minitab to fit a simple linear regression model including residual plots. Are conditions for linear regression satisfied? Answer in terms of Linearity, Independence, Normality and Population standard deviations.

(c) 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?

(d) What is the value of the slope? What does it measure in this scenario?

(e) 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.

(f) Suppose that one of the student 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 -

Your report should consist of sections described below.

Introduction - 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 will be sufficient.

Methods - Include the following:

• A brief description, in your own words, of how the data was collected.
• What type of study was conducted? Name the study design.
• A description of the sample (including the sample size and any demographic information).
• A brief description of variables that you have analysed.
• A list of statistical procedures that you have used.

Results & Discussion - Summarise and discuss 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.
• 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).
• Interpret your statistical findings and discuss their practical significance. In particular, use your results to answer the questions that prompted this study. Are any of the results surprising in any way?
• Indicate shortcomings, if any, of the analyses that were performed. Indicate in particular whether there are any issues with internal and external validity of this study.

There is no word limit. As a guideline, two pages (two and a half at most) will be sufficient, including any tables and graphs. Remember, marks will be awarded for quality not quantity!

Conclusion - What can you conclude from your analysis about sleep, circadian preference and academic performance? Which other factors appear to be important? Explain briefly. There is no word limit. As guideline, one short paragraph will be sufficient. Do not introduce any new information in this section!

Attachment:- Assignment File.rar

Applied Statistics, Statistics

• Category:- Applied Statistics
• Reference No.:- M93130836

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