题目
Problem
The level of sound produced by a particular type of machine was measured for a random sample of 11 such machines. The results, in suitable units, are shown below.
| Machine | A | B | C | D | E | F | G | H | I | J | K |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Sound level | 7.66 | 8.48 | 8.21 | 7.98 | 8.01 | 7.77 | 8.25 | 8.11 | 8.03 | 8.16 | 7.92 |
(a) Use a Wilcoxon signed-rank test to test whether the average sound level produced by this type of machine is more than 8.00. Use a 5% significance level.
[6]
(b) Give a reason why a Wilcoxon signed-rank test may be more appropriate than a -test in this case.
[1]
题目中文翻译
对某种机器随机抽取 11 台，测量它们产生的声音水平。结果以适当单位表示如下。
| 机器 | A | B | C | D | E | F | G | H | I | J | K |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 声音水平 | 7.66 | 8.48 | 8.21 | 7.98 | 8.01 | 7.77 | 8.25 | 8.11 | 8.03 | 8.16 | 7.92 |
(a) 使用 Wilcoxon 符号秩检验，检验这种机器产生的平均声音水平是否大于 8.00。使用 5% 显著性水平。
(b) 说明在这种情况下 Wilcoxon 符号秩检验为什么可能比 检验更合适。