Question 1 Research question: Does average walking speed differ between overweight and non-overweight retirees?Variables to analyse: ‘WSpeed’ and ‘overweight’Draw side-by-side boxplots of walking...

Question 1 Research question: Does average walking speed differ between overweight and non-overweight retirees?Variables to analyse: ‘WSpeed’ and ‘overweight’Draw side-by-side boxplots of walking speed by overweight status.Would you analyse these data using matched sample or independent samples analyses? Explain why. (1 mark)
Question 2 Research question: What is the mean total cholesterol in the population of recent Australian retirees?
Variables to analyse: ‘TCholest’Using R Commander, calculate the 95% confidence interval for the mean total cholesterol in this population
Carefully write in words, what this confidence interval is telling us.
Draw a histogram of total cholesterol. Comment on whether or not the confidence interval in part a) is valid? (That is, are the requirements of the Central Limit Theorem met?) Explain why or why not.
This research question applies to questions 3, 4 and 5.
Research question: Do overweight Australian retirees have higher total cholesterol readings on average than non-overweight Australian retirees?

Variables to analyse: ‘overweight’ and ‘TCholest’
Question 3 Would you address this research question with a one-tailed hypothesis test or a two-tailed hypothesis test? Explain why.
Write the null and alternate hypotheses for a parametric hypothesis test, fully defining any symbols which you use.
Using R Commander find and report .
the mean total cholesterol for overweight retirees in the sample.

the mean total cholesterol for non-overweight retirees in the sample.
the p-value for the difference in mean total cholesterol between these two groups in the population.
Based on the results of c) provide your answer to the research question.
Question 4: Conduct an equivalent nonparametric hypothesis test. Please use R Commander for all calculations, but follow the 5 step method in your presentation. (5 marks)
Question 5 Estimate the minimum sample size required to detect a difference of 1.2 mmol/l in mean total cholesterol between the overweight and non-overweight retirees with α=0.05 and power=0.80 (β=0.20). (That is, this difference could be between 6.8 and 8 mmol/l or between 5.0 and 6.2 mmol/l. You can choose any means as long as they are 1.2 mmol/l apart.) Assume the population standard deviation is σ=3.4 mmol/l and equal group sizes. Present your answer as a sentence which summarises the required sample size to achieve what power subject to what conditions.
Question 6 Research question: Does the proportion of overweight people differ by sex in the Australian retiree population?
Variables to analyse: ‘overweight’ and ‘sex’Show the relationship between overweight and sex 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.
Are the requirements for a Chi-square test met? Explain why.Irrespective of your answer in part b) address the research question using a Chi-square test. (4 marks)
Question 7: Estimate the minimum sample size required to produce a 95% confidence interval with a margin of error of ±6% for the proportion of overweight retirees. Assume that 60% of this population will be overweight. Present your answer as a sentence which summarises the required sample size to achieve what confidence level subject to what conditions.