题目
A school is conducting an experiment to see whether the distance that children can throw a ball increases in hot weather. On a cold day, all the children at the school were asked to throw a ball as far as possible. The distances thrown were measured and recorded. The median distance thrown by a random sample of 25 of the children was 22.0 m. The children were asked to throw the ball again on a hot day. The distances thrown by the same 25 children were measured and recorded and these distances, in m, are shown below.
| 21.2 | 23.5 | 22.9 | 18.6 | 19.4 |
|---|---|---|---|---|
| 22.1 | 26.5 | 20.2 | 25.7 | 20.6 |
| 22.3 | 17.4 | 22.2 | 27.0 | 23.9 |
| 28.2 | 22.6 | 27.2 | 23.0 | 23.7 |
| 19.8 | 22.7 | 23.3 | 21.5 | 24.3 |
The teacher claims that on average the distances thrown will be further when it is hot.
Carry out a Wilcoxon signed-rank test, at the 5% significance level, to test whether the data supports the teacher’s claim.
题目中文翻译
一所学校正在进行实验，研究儿童在炎热天气中投球距离是否会增加。在一个寒冷的日子，学校所有儿童都被要求尽可能远地投球，并测量和记录投球距离。从其中 25 名儿童组成的随机样本中，投球距离的中位数为 22.0 m。随后要求同样的 25 名儿童在炎热的日子再次投球，并测量和记录他们的投球距离。下列数据为这些距离，单位为 m。
| 21.2 | 23.5 | 22.9 | 18.6 | 19.4 |
|---|---|---|---|---|
| 22.1 | 26.5 | 20.2 | 25.7 | 20.6 |
| 22.3 | 17.4 | 22.2 | 27.0 | 23.9 |
| 28.2 | 22.6 | 27.2 | 23.0 | 23.7 |
| 19.8 | 22.7 | 23.3 | 21.5 | 24.3 |
老师声称，平均而言，在炎热天气中投球距离会更远。
在 5% 显著性水平下进行 Wilcoxon 符号秩检验，检验数据是否支持老师的说法。