Introduction to Biostatistics Assignment -

Please answer all 7 questions. Some of the questions require you to analyse the unique assignment data set which I have created for you. Note: Each student will get different answers as the data sets differ.

Question 1 - 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 - 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:

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

b. Write a sentence which answers the research question above as fully as possible.

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 - a. Would you address this research question with a one-tailed hypothesis test or a two-tailed hypothesis test? Explain why.

b. Write the null and alternate hypotheses for a parametric hypothesis test, fully defining any symbols which you use.

c. Using the University of Eastern Sydney data set assigned to you and R Commander find and report

i. the mean wellbeing (WEMWBS) score for drug users in the sample

ii. the mean wellbeing (WEMWBS) score for non-users in the sample

iii. the p-value for the difference in mean wellbeing (WEMWBS) between these two groups in the population

d. Based on the results of c) provide your answer to the research question.

Question 4 - 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.

Question 5 - Suppose that the WEMWBS wellbeing score had been designed to be Normally distributed with a mean μ = 44 and standard deviation σ = 4. 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 α = 0.05 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 - 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:

a. 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.

b. Are the requirements for a Chi-square test met? Explain why.

c. 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.

Question 7 - Estimate the minimum sample size required to produce a 95% confidence interval with a margin of error of ±4% 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.