题目
A college runs academic and vocational courses. The college has 1680 academic students and 2520 vocational students.
(a) Describe how a stratified sample of 70 students at the college could be taken.
All students at the college take a basic skills test. A random sample of 50 academic students has a mean score of 57 and a variance of 60. An independent random sample of 80 vocational students has a mean score of 62 with a variance of 70
(b) Stating your hypotheses clearly, test at the 5% level of significance, whether or not the mean basic skills score for vocational students is greater than the mean basic skills score for academic students.
(c) Explain the importance of the Central Limit Theorem to the test in part (b).
(d) State an assumption that is required to carry out the test in part (b).
All the academic students at the college take a basic skills course. Another random sample of 50 academic students and another independent random sample of 80 vocational students retake the basic skills test. The hypotheses used in part (b) are then tested again at the same level of significance.
The value of the test statistic z is now 1.54
(e) Comment on the mean basic skills scores of academic and vocational students after taking this course.
(f) Considering the outcomes of the tests in part (b) and part (e), comment on the effectiveness of the basic skills course.
题目中文翻译
一所学院开设学术课程和职业课程。该学院有 1680 名学术课程学生和 2520 名职业课程学生。
(a) 说明如何从学院中抽取 70 名学生的分层样本。
学院所有学生都参加基础技能测试。随机抽取的 50 名学术课程学生的平均分为 57，方差为 60。另一个相互独立的 80 名职业课程学生样本的平均分为 62，方差为 70。
(b) 清楚写出假设，在 5% 显著性水平下检验：职业课程学生的基础技能平均分是否大于学术课程学生的基础技能平均分。
(c) 解释中心极限定理在 (b) 中检验中的重要性。
(d) 写出进行 (b) 中检验所需的一条假设。
所有学术课程学生都参加了一门基础技能课程。另取一组 50 名学术课程学生的随机样本，以及一组 80 名职业课程学生的相互独立随机样本，再次参加基础技能测试。随后在同样的显著性水平下检验 (b) 中的假设。
此时检验统计量 的值为 1.54。
(e) 评论接受这门课程后学术课程学生和职业课程学生的平均基础技能分数情况。
(f) 结合 (b) 与 (e) 的检验结果，评论这门基础技能课程的有效性。