题目
A random sample of 13 technology companies is chosen and the numbers of employees in 2018 and in 2022 are recorded.
| Company | A | B | C | D | E | F | G | H | I | J | K | L | M |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Number in 2018 | 104 | 19 | 126 | 234 | 970 | 514 | 35 | 149 | 429 | 12 | 86 | 304 | 1104 |
| Number in 2022 | 106 | 24 | 127 | 228 | 1012 | 525 | 32 | 156 | 449 | 24 | 78 | 294 | 1154 |
A researcher claims that there has been an increase in the median number of employees at technology companies between 2018 and 2022.
(a) Carry out a Wilcoxon matched-pairs signed-rank test, at the 5% significance level, to test whether the data supports this claim.
The researcher notices that the figures for company G have been recorded incorrectly. In fact, the number of employees in 2018 was 32 and the number of employees in 2022 was 35.
(b) Explain, with numerical justification, whether or not the conclusion of the test in part (a) remains the same.
题目中文翻译
随机抽取 13 家科技公司，并记录它们在 2018 年和 2022 年的员工人数。
| 公司 | A | B | C | D | E | F | G | H | I | J | K | L | M |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2018 年人数 | 104 | 19 | 126 | 234 | 970 | 514 | 35 | 149 | 429 | 12 | 86 | 304 | 1104 |
| 2022 年人数 | 106 | 24 | 127 | 228 | 1012 | 525 | 32 | 156 | 449 | 24 | 78 | 294 | 1154 |
一名研究者声称，2018 年到 2022 年间，科技公司的员工人数中位数有所增加。
(a) 在 5% 显著性水平下进行 Wilcoxon 配对符号秩检验，检验这些数据是否支持该声称。
研究者注意到，公司 G 的数据记录有误。事实上，2018 年的员工人数是 32，2022 年的员工人数是 35。
(b) 结合数值说明，解释 (a) 中检验的结论是否保持不变。