题目
Problem
Jade is a swimming instructor at a sports college. She claims that, as a result of an intensive training course, the mean time taken by students to swim 50 metres has reduced by more than 1 second. She chooses a random sample of 10 students. The times taken, in seconds, before and after the training course are recorded in the table.
| Student | A | B | C | D | E | F | G | H | I | J |
|---|---|---|---|---|---|---|---|---|---|---|
| Time before course | 54.2 | 47.4 | 52.1 | 59.0 | 55.3 | 51.0 | 48.9 | 52.2 | 58.4 | 51.4 |
| Time after course | 50.1 | 46.3 | 52.5 | 58.8 | 51.4 | 48.4 | 49.5 | 48.7 | 58.3 | 51.4 |
(a) Test, at the 10% significance level, whether Jade’s claim is justified.
[7]
(b) State an assumption that is necessary for this test to be valid.
[1]
题目中文翻译
Jade 是一所体育学院的游泳教练。她声称，经过一次强化训练课程后，学生游 50 米所用的平均时间减少了超过 1 秒。她随机抽取 10 名学生。训练课程前后所用的时间如下表，单位为秒。
| 学生 | A | B | C | D | E | F | G | H | I | J |
|---|---|---|---|---|---|---|---|---|---|---|
| 训练前时间 | 54.2 | 47.4 | 52.1 | 59.0 | 55.3 | 51.0 | 48.9 | 52.2 | 58.4 | 51.4 |
| 训练后时间 | 50.1 | 46.3 | 52.5 | 58.8 | 51.4 | 48.4 | 49.5 | 48.7 | 58.3 | 51.4 |
(a) 在 10% 显著性水平下，检验 Jade 的声称是否合理。
(b) 说明使该检验有效所需要的一个假设。