题目
Problem
At a dog show, 5 Great Dane dogs were ranked by two judges, judge X and judge Y.
Spearman’s rank correlation coefficient between the judges’ ranks is calculated and a test for positive correlation is carried out at the 5% significance level.
(a) State suitable hypotheses for the test.
Given that the result of the hypothesis test was to reject H0,
(b) show that the largest possible value of ∑d^2 is 2.
The table below gives the rank order for judge X.
| Dog | A | B | C | D | E |
|---|---|---|---|---|---|
| Judge X | 1 | 2 | 3 | 4 | 5 |
Given that ∑d^2 takes its largest possible value,
(c) find a possible order for judge Y’s rankings.
(6)
(Total for Question 2 is 6 marks)
题目中文翻译
在一场狗展中，5 只大丹犬由两位评委 X 和 Y 进行排名。
已计算出两位评委排名的 Spearman 秩相关系数，并在 5% 的显著性水平下进行正相关检验。
(a) 写出适合该检验的假设。
已知该假设检验的结果是拒绝 H0。
(b) 证明 ∑d^2 的最大可能值为 2。
下表给出了评委 X 的排名顺序。
| 狗 | A | B | C | D | E |
|---|---|---|---|---|---|
| 评委 X | 1 | 2 | 3 | 4 | 5 |
已知 ∑d^2 取到最大可能值，
(c) 写出评委 Y 的一种可能排名顺序。