题目
Problem
At a local talent show 2 judges were asked to rank 10 performances, in order of preference. The results are shown in the following table.
| Performance | A | B | C | D | E | F | G | H | I | J |
|---|---|---|---|---|---|---|---|---|---|---|
| Judge 1 | 1 | 3 | 5 | 7 | 9 | 10 | 2 | 6 | 8 | 4 |
| Judge 2 | 2 | 1 | 3 | 7 | 9 | 4 | 5 | 8 | 10 | 6 |
(a) Calculate Spearman’s rank correlation coefficient for these data. Show your working clearly.
(b) Stating your hypotheses clearly, test at the 1% level of significance, whether or not there is evidence of a positive correlation between the ranks of Judge 1 and the ranks of Judge 2.
(7)
(Total for Question 2 is 7 marks)
题目中文翻译
在一场地方才艺表演中，两位评委被要求按喜好顺序对 10 个表演进行排名。结果如下表所示。
| 表演 | A | B | C | D | E | F | G | H | I | J |
|---|---|---|---|---|---|---|---|---|---|---|
| 评委 1 | 1 | 3 | 5 | 7 | 9 | 10 | 2 | 6 | 8 | 4 |
| 评委 2 | 2 | 1 | 3 | 7 | 9 | 4 | 5 | 8 | 10 | 6 |
(a) 计算这些数据的 Spearman 秩相关系数，并清楚写出过程。
(b) 清楚写出假设，在 1% 的显著性水平下检验两位评委的排名之间是否有正相关证据。