6 The manager of a technology company \(A\) claims that his employees earn more per year than the employees at technology company \(B\). The amounts earned per year, in hundreds of dollars, by a random sample of 12 employees from company \(A\) and an independent random sample of 12 employees from company \(B\) are shown below.
| Company \(A\) | 461 | 482 | 374 | 512 | 415 | 452 | 502 | 427 | 398 | 545 | 612 | 359 |
| Company \(B\) | 454 | 506 | 491 | 384 | 361 | 443 | 401 | 472 | 414 | 342 | 355 | 437 |
- Carry out a Wilcoxon rank-sum test at the \(5 \%\) significance level to test whether the manager's claim is supported by the data.
- Explain whether a paired sample \(t\)-test would be appropriate to test the manager's claim if earnings are normally distributed.
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