题目
A large college is holding a piano competition. Each student has played a particular piece of music and two judges have each awarded a mark out of 80. The marks awarded to a random sample of 14 students are shown in the following table.
| Student | A | B | C | D | E | F | G | H | I | J | K | L | M | N |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Judge 1 | 79 | 54 | 63 | 74 | 69 | 52 | 50 | 57 | 55 | 42 | 63 | 55 | 56 | 48 |
| Judge 2 | 75 | 62 | 60 | 73 | 76 | 41 | 31 | 51 | 45 | 55 | 49 | 50 | 65 | 36 |
(a) One of the students claims that on average Judge 1 is awarding higher marks than Judge 2. Carry out a Wilcoxon matched-pairs signed-rank test at the 5% significance level to test whether the data supports the student’s claim.
(b) Give a reason why it is preferable to use a Wilcoxon matched-pairs signed-rank test in this situation rather than a paired sample -test.
题目中文翻译
一所大型学院正在举办钢琴比赛。每位学生演奏了一首指定乐曲，两位评委分别给出满分 80 分的评分。下表给出了随机抽取的 14 名学生所得的分数。
| 学生 | A | B | C | D | E | F | G | H | I | J | K | L | M | N |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 评委 1 | 79 | 54 | 63 | 74 | 69 | 52 | 50 | 57 | 55 | 42 | 63 | 55 | 56 | 48 |
| 评委 2 | 75 | 62 | 60 | 73 | 76 | 41 | 31 | 51 | 45 | 55 | 49 | 50 | 65 | 36 |
(a) 其中一名学生声称，平均而言评委 1 给出的分数高于评委 2。使用 Wilcoxon 配对符号秩检验，在 5% 显著性水平下检验数据是否支持该学生的说法。
(b) 说明为什么在这种情况下使用 Wilcoxon 配对符号秩检验比使用配对样本 检验更合适。