Problem 3: 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 occassions 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 1-3, you may assume that run times are distributed normally within each group.

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

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

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

For parts 4-5, make no assumptions about the distribution of run times.

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

5. 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)

runnerID group avg.time.march avg.time.may

538981 placebo 51.02 47.46

487418 placebo 54.81 55.74

286045 placebo 41.65 41.18

493204 placebo 42.87 45.64

173721 placebo 51.65 47.1

195407 placebo 35.69 35.39

585182 placebo 42.14 41.49

237905 placebo 35.66 32.55

302261 placebo 45.29 44.23

518645 placebo 40.09 39.08

549853 placebo 46.31 50.01

582901 placebo 35.98 33.2

540736 placebo 39.89 39.76

419288 placebo 36.74 34.11

268178 placebo 43.18 43.86

567417 placebo 38.1 40.13

114031 placebo 39.2 33.77

510203 placebo 34.36 33.22

572901 placebo 39.74 37.92

370850 placebo 46.09 41.13

580193 placebo 45.31 38.39

300312 placebo 49.75 49.17

248404 placebo 40.63 41.54

211913 placebo 49.8 45.14

380646 placebo 35.71 38.2

417512 supplement 30.35 30.31

100170 supplement 59.97 54.81

245525 supplement 36.2 32.57

246461 supplement 43.04 45.12

176309 supplement 33.5 35.2

522926 supplement 40.35 40.91

442016 supplement 39.95 38.38

222524 supplement 27.62 25

192381 supplement 45.06 36.9

461875 supplement 25.35 27.06

407617 supplement 58.25 52.63

381069 supplement 30.33 22.45

277817 supplement 38.59 39.32

554371 supplement 36.6 36.96

316620 supplement 35.89 34.07

545055 supplement 42.51 37.04

420860 supplement 28.13 24.12

447507 supplement 32.14 29.65

376204 supplement 30.36 29.03

355561 supplement 39.14 38.32

169922 supplement 24.93 19.76

282432 supplement 28.3 25.21

427407 supplement 22.14 17.2

497388 supplement 48.33 43.02

510909 supplement 56.52 56.48