题目
Problem
The table shows the time, in seconds, of the fastest qualifying lap for 10 different Formula One racing drivers and their finishing position in the actual race.
| Driver | A | B | C | D | E | F | G | H | I | J |
|---|---|---|---|---|---|---|---|---|---|---|
| Fastest qualifying lap | 62.94 | 63.92 | 63.63 | 62.95 | 63.97 | 63.87 | 64.31 | 64.64 | 65.18 | 64.21 |
| Finishing position | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
(a) Calculate the value of Spearman’s rank correlation coefficient for these data.
(4)
(b) Stating your hypotheses clearly, test at the 1% level of significance, whether or not there is evidence of a positive correlation between the fastest qualifying lap time and finishing position for these Formula One racing drivers.
(4)
题目中文翻译
下表给出了 10 位不同的一级方程式赛车手最快排位赛圈速的时间（单位：秒），以及他们在正式比赛中的完赛名次。
| 车手 | A | B | C | D | E | F | G | H | I | J |
|---|---|---|---|---|---|---|---|---|---|---|
| 最快排位赛圈速 | 62.94 | 63.92 | 63.63 | 62.95 | 63.97 | 63.87 | 64.31 | 64.64 | 65.18 | 64.21 |
| 完赛名次 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
(a) 计算这些数据的斯皮尔曼等级相关系数。
(b) 清楚写出假设，在 1% 显著性水平下检验：对于这些一级方程式赛车手，最快排位赛圈速与完赛名次之间是否有正相关证据。