题目
A large company surveyed its staff to investigate the awareness of company policy.
The company employs 6000 full-time staff and 4000 part-time staff.
(a) Describe how a stratified sample of 200 staff could be taken.
(b) Explain an advantage of using a stratified sample rather than a simple random sample.
A random sample of 80 full-time staff and an independent random sample of 80 part-time staff were given a test of policy awareness. The results are summarised in the table below.
| Mean score () | Variance of scores () | |
|---|---|---|
| Full-time staff | 52 | 21 |
| Part-time staff | 50 | 19 |
(c) Stating your hypotheses clearly, test, at the 1% level of significance, whether or not the mean policy awareness scores for full-time and part-time staff are different.
(d) Explain the significance of the Central Limit Theorem to the test in part (c).
(e) State an assumption you have made in carrying out the test in part (c).
After all the staff had completed a training course the 80 full-time staff and the 80 part-time staff were given another test of policy awareness. The value of the test statistic was 2.53
(f) Comment on the awareness of company policy for the full-time and part-time staff in light of this result. Use a 1% level of significance.
(g) Interpret your answers to part (c) and part (f).
题目中文翻译
一家公司调查员工对公司政策的了解程度。
该公司有 6000 名全职员工和 4000 名兼职员工。
(a) 说明如何抽取 200 名员工的分层样本。
(b) 说明与简单随机样本相比，使用分层样本的一个优点。
从 80 名全职员工和一个独立的 80 名兼职员工随机样本中，给他们做了一项政策认知测试。结果如下表所示。
| 平均分 (x̄) | 分数方差 (s^2) | |
|---|---|---|
| 全职员工 | 52 | 21 |
| 兼职员工 | 50 | 19 |
(c) 清楚写出假设，在 1% 的显著性水平下检验全职和兼职员工的平均政策认知分数是否不同。
(d) 说明中央极限定理对 (c) 中检验的意义。
(e) 写出在 (c) 中进行检验时所作出的一个假设。
在所有员工完成培训课程后，这 80 名全职员工和 80 名兼职员工又进行了另一项政策认知测试。检验统计量 z 的值为 2.53。
(f) 在 1% 的显著性水平下，根据该结果评论全职和兼职员工的政策认知情况。
(g) 解释 (c) 和 (f) 的答案。