题目
Seven athletes compete in a 200 m race and a 400 m race.
Their 200 m times are shown below.
| Athlete | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| 200 m time / s | 23.4 | 23.1 | 22.9 | 23.7 | 27.6 | 24.4 | 24.1 |
The order of finishing in the 400 m race is A, B, G, C, D, F, E.
(a) Calculate Spearman’s rank correlation coefficient between the finishing order in the 200 m race and the finishing order in the 400 m race.
(b) Test, at the 5% level of significance, for a positive correlation between the finishing order in the 200 m race and the finishing order in the 400 m race.
Their long jump results are shown below.
| Athlete | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| Long jump / m | 6.50 | 6.47 | 6.12 | 6.12 | 6.48 | 6.38 | 6.47 |
(c) Without any further calculations, explain how to obtain Spearman’s rank correlation coefficient between the finishing order in the 200 m race and the long jump order.
题目中文翻译
7 名运动员参加了 200 m 和 400 m 两项比赛。
他们的 200 m 用时如下。
| 运动员 | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| 200 m 用时 / s | 23.4 | 23.1 | 22.9 | 23.7 | 27.6 | 24.4 | 24.1 |
400 m 比赛的完赛顺序是 A、B、G、C、D、F、E。
(a) 计算 200 m 比赛完赛顺序与 400 m 比赛完赛顺序之间的 Spearman 秩相关系数。
(b) 在 5% 显著性水平下，检验 200 m 比赛完赛顺序与 400 m 比赛完赛顺序之间是否存在正相关。
他们的跳远成绩如下。
| 运动员 | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| 跳远 / m | 6.50 | 6.47 | 6.12 | 6.12 | 6.48 | 6.38 | 6.47 |
(c) 不做任何进一步计算，说明如何求 200 m 比赛完赛顺序与跳远顺序之间的 Spearman 秩相关系数。