题目
Nine athletes in a club have a new coach. The coach adopts a new training programme which he believes will reduce the race times of these athletes. Each athlete completes a 1500 m time trial before and after completing the new training programme. Their times, in seconds (s), are recorded.
| Athlete | A | B | C | D | E | F | G | H | I |
|---|---|---|---|---|---|---|---|---|---|
| Time before training (s) | 250 | 251 | 252 | 267 | 276 | 291 | 310 | 320 | 335 |
| Time after training (s) | 245 | 251 | 253 | 261 | 275 | 293 | 302 | 313 | 320 |
(a) Carry out a paired t-test at the 5% significance level to test the coach’s belief.
Further research suggests that the effects of the training programme tend to reduce the times of the slower athletes by more than those of the faster athletes.
(b) Suggest a reason why the paired t-test used in part (a) may not have been an appropriate test in this case.
(c) Suggest a suitable alternative test that could have been used instead of a paired t-test.
题目中文翻译
某俱乐部的 9 名运动员有了一位新教练。教练采用了一个新的训练计划，他认为该计划会减少这些运动员的比赛用时。每名运动员在完成新训练计划前后各完成一次 1500 m 计时测试。他们的用时（秒）如下。
| 运动员 | A | B | C | D | E | F | G | H | I |
|---|---|---|---|---|---|---|---|---|---|
| 训练前用时 (s) | 250 | 251 | 252 | 267 | 276 | 291 | 310 | 320 | 335 |
| 训练后用时 (s) | 245 | 251 | 253 | 261 | 275 | 293 | 302 | 313 | 320 |
(a) 在 5% 显著性水平下进行配对 t 检验，以检验教练的看法。
进一步研究表明，该训练计划的效果倾向于使较慢运动员的用时减少得比较快运动员更多。
(b) 说明为什么(a)中使用的配对 t 检验在这种情况下可能不是合适的检验。
(c) 提出一种可以替代配对 t 检验的合适检验。