题目
Secondary schools in a region conduct ability testing at the start of Year 7 and the start of Year 8. Each year a regional education officer randomly selects 240 Year 7 students and 240 Year 8 students from across the region. The results for last year are summarised in the table below.
| Mean score | Variance of scores | |
|---|---|---|
| Year 7 | 101 | 38 |
| Year 8 | 103 | 42 |
The regional education officer claims that there is no difference between the mean scores of these two year groups.
(a) Test the regional education officer’s claim at the 1% significance level. You should state your hypotheses, test statistic and critical value clearly.
(b) Explain the significance of the Central Limit Theorem in part (a).
题目中文翻译
某地区的中学在 7 年级开始和 8 年级开始时进行能力测试。 每年，一名地区教育官员随机从全区抽取 240 名 7 年级学生和 240 名 8 年级学生。 去年的结果汇总如下表。
| 平均分 | 分数方差 | |
|---|---|---|
| 7 年级 | 101 | 38 |
| 8 年级 | 103 | 42 |
该地区教育官员声称，这两个年级组的平均分没有差异。
(a) 在 1% 显著性水平下检验该说法。请清楚写出原假设、检验统计量和临界值。
(b) 解释 (a) 小题中中心极限定理的意义。