题目
A professor claims that undergraduates studying History have a typing speed of more than 15 words per minute faster than undergraduates studying Maths.
A sample is taken of 38 undergraduates studying History and 45 undergraduates studying Maths. The typing speed, x words per minute, of each undergraduate is recorded. The results are summarised in the table below.
| n | x | s^2 | |
|---|---|---|---|
| Undergraduates studying History | 38 | 56.3 | 27.2 |
| Undergraduates studying Maths | 45 | 39.8 | 18.5 |
(a) Use a suitable test, at the 5% level of significance, to investigate the professor’s claim. State clearly your hypotheses, test statistic and critical value.
(b) State two assumptions you have made in carrying out the test in part (a).
题目中文翻译
一位教授声称，学习历史的本科生打字速度比学习数学的本科生每分钟快 15 个词以上。
抽取了 38 名学习历史的本科生和 45 名学习数学的本科生作为样本。 每位本科生的打字速度 x（每分钟词数）都被记录下来。结果汇总如下表。
| n | x | s^2 | |
|---|---|---|---|
| 学习历史的本科生 | 38 | 56.3 | 27.2 |
| 学习数学的本科生 | 45 | 39.8 | 18.5 |
(a) 在 5% 显著性水平下，使用适当的检验来调查教授的说法。 请清楚写出你的原假设、检验统计量和临界值。
(b) 写出在完成 (a) 小题检验时所作的两个假设。