Introduction to Biostatistics Assignment -
Please answer all 7 questions. 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) scorefor 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 Commanderfind 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 difference 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 ofillicit 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.
Description of your data set -
This data file presents measurements from a random sample of 273 students from the University of Eastern Sydney. (But please remember that this is a completely artificial data file. It does not reflect any real world measurements or associations.)
Within R Commander the data set is called 'alcohol'.
There are 273 lines of data.
Attachment:- Assignment Files.rar