Set by Dr. Daniel Perley

Problem : Runner's Regimen (Please post your answers with R command lines used)

A group of 50 runners are enrolled in a study on the effects of taking a particular supplement on their fitness. During March, they are asked to run a 5-km run on 10 separate occasions and record their times, which were averaged together and the value recorded in the file runners.csv. The supplement, or a placebo, is taken daily during April. In May, they are again asked to run a 5-km run on 10 occasions and record their average times.

For parts a-c, you may assume that run times are distributed normally within each group.

a. Did the times of runners in the placebo group become significantly shorter, or significantly longer, between March and May? Provide a p-value.

b. Did the times of runners taking the supplement become significantly shorter, or significantly longer, between March and May? Provide a p-value.

c. Can you conclude that the supplement was effective at improving run times, in comparison to the placebo? Provide a p-value. [3]

For parts d-e, make no assumptions about the distribution of run times.

d. Calculate the sample interquartile range of run times for all runners in March.

e. Use a percentile bootstrap (or another bootstrap) to provide a 95% confidence interval on the population interquartile range for all runners in March. Use at least 10000 bootstrap iterations.

runners.csv ( save this data as CSV on your machine)

https://1drv.ms/u/s!AgOhBzX2T2W6ux8ELwHe7iymjYde?e=YYbBNF