Question 3 (17 marks) In a study on the effect of caffeine on muscle metabolism, nine male volunteers from a random group of men underwent arm exercise tests on two separate occasions. On one occasion the volunteer took a placebo capsule an hour before the test; on the other occasion he received a capsule containing caffeine. The order of these treatments was randomised for each participant. During each exercise test, the ratio of carbon dioxide produced to oxygen consumed (respiratory exchange ratio or "%RER") was measured

The data are as follows: Volunteer 1 2 3 4 5 6 7 8 9 Placebo: 105 109 93 99 96 101 96 95 98 Caffeine: 96 99 89 95 88 95 88 93 88

a) Are these data paired or unpaired? Explain briefly the advantages of this type of study design. b) Calculate the relevant summary statistics from the data? (calculator may be needed) c) What conditions are needed to proceed with inference using this data? What type of plot would be necessary as a check? Perform a basic, quick check to show that the conditions are valid. d) Calculate a 90% confidence interval for the mean change in %RER with use of caffeine. Show all of your working. e) Based on that confidence interval, is there sufficient evidence to conclude that caffeine consumption affects the mean % RER? f) Conduct a test of significance (at a significance level of 5%) to determine if there is evidence of a difference in % RER between the two treatment groups: placebo and caffeine.

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