题目
A school with a large number of students is updating its logo. Each student has designed a new logo and two teachers have each awarded a mark out of 50 for each logo. The marks awarded to a random sample of 12 students are shown in the following table.
| Student | A | B | C | D | E | F | G | H | I | J | K | L |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Teacher 1 | 36 | 38 | 40 | 36 | 22 | 34 | 45 | 44 | 48 | 35 | 28 | 30 |
| Teacher 2 | 38 | 42 | 32 | 41 | 32 | 41 | 42 | 50 | 36 | 44 | 42 | 41 |
One of the students claims that Teacher 2 is awarding higher marks than Teacher 1.
(a) Carry out a Wilcoxon matched-pairs signed-rank test, at the 5% significance level, to test whether the data supports the claim.
It was later discovered that Teacher 1 had entered her mark for student C incorrectly. Her intended mark was 24 not 40. This was corrected.
(b) Determine whether this correction affects the conclusion of the test carried out in part (a).
题目中文翻译
一所拥有大量学生的学校正在更新其校徽。每名学生都设计了一个新校徽，两名教师分别给每个校徽打出满分 50 分的分数。随机抽取 12 名学生，所得分数如下表所示。
| 学生 | A | B | C | D | E | F | G | H | I | J | K | L |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 教师 1 | 36 | 38 | 40 | 36 | 22 | 34 | 45 | 44 | 48 | 35 | 28 | 30 |
| 教师 2 | 38 | 42 | 32 | 41 | 32 | 41 | 42 | 50 | 36 | 44 | 42 | 41 |
其中一名学生声称教师 2 给出的分数高于教师 1。
(a) 在 5% 显著性水平下进行 Wilcoxon 配对符号秩检验，以检验数据是否支持该声称。
后来发现，教师 1 错误地输入了学生 C 的分数。她原本想输入的分数是 24，而不是 40。这个错误已被更正。
(b) 判断这一更正是否会影响(a)中检验的结论。