题目
Problem
A large number of students took two test papers in mathematics. The teacher believes that the marks obtained in Paper 1 will be higher than the marks obtained in Paper 2. She chooses a random sample of 9 students and compares their marks. The marks are shown in the table.
| Student | A | B | C | D | E | F | G | H | I |
|---|---|---|---|---|---|---|---|---|---|
| Paper 1 | 46 | 73 | 55 | 64 | 86 | 42 | 66 | 68 | 60 |
| Paper 2 | 41 | 66 | 61 | 63 | 90 | 40 | 58 | 42 | 70 |
(a) Carry out a Wilcoxon matched-pairs signed-rank test, at the 5% significance level, to test whether the data supports the teacher’s belief.
[7]
(b) State an assumption that you have made in carrying out the test in part (a).
[1]
题目中文翻译
大量学生参加了两份数学测试卷。老师认为 Paper 1 的得分会高于 Paper 2 的得分。她随机抽取 9 名学生并比较他们的分数。分数如下表所示。
| 学生 | A | B | C | D | E | F | G | H | I |
|---|---|---|---|---|---|---|---|---|---|
| Paper 1 | 46 | 73 | 55 | 64 | 86 | 42 | 66 | 68 | 60 |
| Paper 2 | 41 | 66 | 61 | 63 | 90 | 40 | 58 | 42 | 70 |
(a) 在 5% 显著性水平下，进行 Wilcoxon 配对符号秩检验，检验数据是否支持老师的看法。
(b) 说明你在进行 part (a) 中的检验时所作的一个假设。