题目
A statistics course was taught by two professors. Students attend either all lectures given by professor A or all lectures given by professor B.
Students who took this course all sat the same examination at the end of the course and their mark, x, was recorded.
The results of the examination for a random sample of students taught by each professor are summarised in the table below.
| n | ∑x | ∑x^2 | Unbiased estimate of the mean | Unbiased estimate of the variance | |
|---|---|---|---|---|---|
| Students taught by professor A | 50 | 3610 | 260955.6 | 72.2 | 6.4 |
| Students taught by professor B | 50 | 3085 | 190457.2 | m | v |
(a) Find the value of m and the value of v.
The head of department claims that the mean mark of the students taught by professor A is more than 10 marks greater than the mean mark of the students taught by professor B.
(b) Use a suitable test, at the 5% level of significance, to investigate the claim made by the head of department.
(c) State two assumptions you have made in carrying out the test in part (b).
题目中文翻译
某统计课程由两位教授授课。学生要么全部听教授 A 的课，要么全部听教授 B 的课。
参加该课程的学生都在课程结束时参加同一场考试，并记录了他们的分数 x。
下表汇总了由两位教授分别教学的一个随机样本学生的考试结果。
| n | ∑x | ∑x^2 | 均值的无偏估计 | 方差的无偏估计 | |
|---|---|---|---|---|---|
| 教授 A 的学生 | 50 | 3610 | 260955.6 | 72.2 | 6.4 |
| 教授 B 的学生 | 50 | 3085 | 190457.2 | m | v |
(a) 求 m 和 v。
系主任声称，教授 A 所教学生的平均分比教授 B 所教学生的平均分高 10 分以上。
(b) 使用适当的检验，在 5% 显著性水平下检验系主任的说法。
(c) 写出在 (b) 中做检验时所作的两个假设。