14.
Nine long-distance runners are starting an exercise programme to improve their strength. During the first session, each of them has to do a 100 metre run and to do as many push-ups as possible in one minute. The times taken for the run, together with the number of push-ups each runner achieves, are shown in the table.
| Runner | A | B | C | D | E | F | G | H | I |
| 100 metre time (seconds) | 13.2 | 11.6 | 10.9 | 12.3 | 14.7 | 13.1 | 11.7 | 13.6 | 12.4 |
| Push-ups achieved | 32 | 42 | 22 | 36 | 41 | 27 | 37 | 38 | 33 |
- Calculate the value of Spearman's rank correlation coefficient.
- Carry out a hypothesis test at the \(5 \%\) significance level to examine whether there is any association between time taken for the run and number of push-ups achieved. [4]
- Under what circumstances is it appropriate to carry out a hypothesis test based on the product moment correlation coefficient. State, with a reason, which test is more appropriate for these data.