题目
A company is deciding which of two machines, and , can make a certain type of electrical component more quickly. The times taken, in minutes, to make one component of this type are recorded for a random sample of 8 components made by machine and a random sample of 9 components made by machine . These times are as follows.
| Machine | 4.0 | 4.6 | 4.7 | 4.8 | 5.0 | 5.2 | 5.6 | 5.8 | |
|---|---|---|---|---|---|---|---|---|---|
| Machine | 4.5 | 4.9 | 5.1 | 5.3 | 5.4 | 5.7 | 5.9 | 6.3 | 6.4 |
The manager claims that on average the time taken by machine to make one component is less than that taken by machine .
(a) Carry out a Wilcoxon rank-sum test at the 5% significance level to test whether the manager’s claim is supported by the data.
(b) Assuming that the times taken to produce the components by the two machines are normally distributed with equal variances, carry out a -test at the 5% significance level to test whether the manager’s claim is supported by the data.
(c) In general, would you expect the conclusions from the tests in parts (a) and (b) to be the same? Give a reason for your answer.
题目中文翻译
一家公司正在判断两台机器 和 中哪一台能更快地生产某种电气元件。分别从机器 生产的 8 个元件和机器 生产的 9 个元件中随机抽样，记录生产一个这种元件所需的时间，单位为分钟。数据如下。
| 机器 | 4.0 | 4.6 | 4.7 | 4.8 | 5.0 | 5.2 | 5.6 | 5.8 | |
|---|---|---|---|---|---|---|---|---|---|
| 机器 | 4.5 | 4.9 | 5.1 | 5.3 | 5.4 | 5.7 | 5.9 | 6.3 | 6.4 |
经理声称，平均而言，机器 生产一个元件所需的时间少于机器 。
(a) 在 5% 显著性水平下进行 Wilcoxon 秩和检验，检验数据是否支持经理的说法。
(b) 假设两台机器生产元件所需时间均服从正态分布且方差相等，在 5% 显著性水平下进行 检验，检验数据是否支持经理的说法。
(c) 一般来说，你是否预期 (a) 和 (b) 两部分检验的结论相同？给出理由。