Please answer all 7 questions. Record your answers in the template document provided and submit via Turnitin before 11:59pm on the due date. The marks allocated to each question are shown in the assignment.  A total of 30 marks are available and this assignment is worth 30% of your overall grade.

Some of the questions require you to analyse the unique assignment data set which I have created for you. This is labelled ‘dataforxxxxxxxx.RData’ where xxxxxxxx represents your Student ID number. You can find this with your Assessment materials in vUWS. Please also locate and read ‘Description of your data set.docx’.

Note: Each student will get different answers as the data sets differ.

Question 1 (5 marks)

A random sample of 10 former University of Eastern Sydney students was ask whether they drink more or less since they graduated from University. Their answers were:

more, less, less, less, more, less, less, less, less, more

Conduct a sign test to see whether or not this provides evidence of a change in drinking habits of the wider population of graduates from University of Eastern Sydney. Use the 5-step method and show all working. Use the Table 6 from the textbook (below) to determine the decision rule or use R Commander to calculate the p-value.

Question 2 (3 marks)

Research question: What is the mean well-being (WEMWBS) score for University of Eastern Sydney Students?

Using the University of Eastern Sydney data set assigned to you and R Commander:

• Calculate the 95% confidence interval for the mean well-being (WEMWBS) score in this population. (1 mark)

• Write a sentence which answers the research question above as fully as possible. (2 marks).

This research question applies to questions 3 and 4

Research question: Among University of Eastern Sydney students, do self-reporting drug users (variable: drug) have lower well-being scores (variable: WEMWBS) than non-users?

Question 3 (7 marks)

• Would you address this research question with a one-tailed hypothesis test or a two-tailed hypothesis test? Explain why. (1 mark)

• Write the null and alternate hypotheses for a parametric hypothesis test, fully defining any symbols which you use. (2 marks)

• Using the University of Eastern Sydney data set assigned to you and R Commander find and report (2 marks)
  • the mean wellbeing (WEMWBS) score for drug users in the sample
  • the mean wellbeing (WEMWBS) score for non-users in the sample
  • the p-value for the difference in mean wellbeing (WEMWBS) between these two groups in the population

• Based on the results of c) provide your answer to the research question. (2 marks)

Question 4 (5 marks)

Conduct an equivalent nonparametric hypothesis test for this research question. Please use R Commander for all calculations, but follow the 5 step method in your presentation. (5 marks)

Question 5 (3 marks)

Suppose that the WEMWBS wellbeing score had been designed to be Normally distributed with a mean  and standard deviation .  Suppose we wished to undertake a study to test whether the mean wellbeing (WEMWBS) score of Western Sydney University students was at least half a standard deviation (2 points) better than average. Suppose we wished the test to return 90% power of detecting a higher mean score of this size at the  significance level. Use an appropriate online calculator to calculate the minimum required sample size for this study. Present your answer as a sentence which details the required sample size to achieve what power subject to what conditions.

Question 6 (5 marks)

Research question: Does the proportion of students self-reporting as illicit drugs users differ by gender in the University of Eastern Sydney population?

Using the University of Eastern Sydney data set assigned to you and R Commander:

• Show the relationship between illicit drug use and gender using a two-way contingency table. Include either row or column percentages. Type and label the table yourself; an R Commander screenshot will not be accepted. (1 mark)

• Are the requirements for a Chi-square test met? Explain why. (1 mark)

• Irrespective of your answer in part b. address the research question using a Chi-square test. Ensure you specify the hypotheses you are testing and explain the evidence for or against the hypothesis. (3 marks)

Question 7 (2 marks)

Estimate the minimum sample size required to produce a 95% confidence interval with a margin of error of for the proportion of illicit drug users among Western Sydney University students. Present your answer as a sentence which summarises the required sample size to achieve what confidence level subject to what conditions.

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