Question 1

1. Using R Commander and the data set assigned to you, calculate and interpret the 95% confidence interval for the mean SF36 mental health score (variable 'mh') in the population of full-time workers in Sydney. That is, write your answer in one or two sentence stating the confidence interval and what it means. Don't forget to check any assumptions underlying your method.

1. Looking at the confidence interval from part a) alone, is the mean SF36 mental health score (variable 'mh') in the population of full-time workers in Sydney statistically significantly different from 66 at the 0.05 significance level? Explain why or why not.

1. Using the data set assigned to you, test the hypothesis that mean SF36 mental health score (variable 'mh') differs between males and females (variable 'sex') in the population of full-time workers in Sydney. Use the appropriate t-test and explain why a t-test is valid. Use R Commander to do all calculations but present your answer following the 5 step method, defining any symbols you use.

1. Repeat part c) using a non-parametric test. Use R Commander to do all calculations but present your answer following the 5 step method, defining any symbols you use.

Question 2

1. Using the data set assigned to you, test the hypothesis that the proportion of full-time workers in Sydney who work in the public sector (variable 'sector') is less than 0.15. Check any assumptions required by the probability model. Use R Commander to do all calculations but present your answer following the 5 step method, defining any symbols you use.

1. Using the data set assigned to you and R Commander, calculate and interpret the 95% confidence interval for the difference between the proportion of Sydney full-time workers in the government sector (variable 'sector') who speak English at home (variable 'lang') and the proportion of Sydney full-time workers in the private sector who speak English at home.

Question 4

1. Using the data set assigned to you and R Commander, calculate the proportion of males in the sample whose working hours are recorded as 'unable to work' (variable 'work-impact').

1. Suppose we wished to have at least 80% power at the ?=0.05 significance level to detect a difference of 0.05 in the proportion of males and females who are 'unable to work' due to the lockdown. Using the proportion of males 'unable to work' observed in part a) and adding or subtracting 0.05 for females, estimate the minimum sample size required to test for a clinically significant difference in rate of males and females 'unable to work' in a population of Sydney full-time workers, with 80% power at the ?=0.05 significance level. Assume there will be equal numbers of males and females.

1. Using R Commander and the data set assigned to you, calculate the standard deviation of SF36 mental health score (variable 'mh') in the sample of full-time workers in Sydney provided to you.

1. Using the result in c) estimate the minimum sample size required to produce a 95% confidence interval for the mean SF36 mental health score in the population of full-time workers in Sydney which has a margin of error of 1.5 kgs. Present your answer as a sentence which summarises the required sample size and under what conditions.

1. Describe one disadvantage of using a 50% confidence interval rather than a 95% confidence interval.

Question 3

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