题目
Problem
The manager of a technology company claims that his employees earn more per year than the employees at technology company . The amounts earned per year, in hundreds of dollars, by a random sample of 12 employees from company and an independent random sample of 12 employees from company are shown below.
| Company | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 461 | 482 | 374 | 512 | 415 | 452 | 502 | 427 | 398 | 545 | 612 | 359 | |
| 454 | 506 | 491 | 384 | 361 | 443 | 401 | 472 | 414 | 342 | 355 | 437 |
(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.
[9]
(b) Explain whether a paired sample -test would be appropriate to test the manager’s claim if earnings are normally distributed.
[1]
题目中文翻译
科技公司 的经理声称，他的员工每年收入高于科技公司 的员工。下表给出了从公司 随机抽取的 12 名员工，以及从公司 独立随机抽取的 12 名员工的年收入，单位为百美元。
| 公司 | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 461 | 482 | 374 | 512 | 415 | 452 | 502 | 427 | 398 | 545 | 612 | 359 | |
| 454 | 506 | 491 | 384 | 361 | 443 | 401 | 472 | 414 | 342 | 355 | 437 |
(a) 在 5% 显著性水平下进行 Wilcoxon 秩和检验，检验数据是否支持该经理的说法。
(b) 如果收入服从正态分布，说明配对样本 检验是否适合用于检验该经理的说法。