题目
A manager of a large company is investigating the time it takes the company’s employees to complete a task.
The manager believes that the mean time for full-time employees to complete the task is more than a minute quicker than the mean time for part-time employees to complete the task.
The manager collects a random sample of 605 full-time employees and 45 part-time employees and records the times, t minutes, it takes each employee to complete the task. The results are summarised in the table below.
| n | t | s^2 | |
|---|---|---|---|
| Full-time employees | 605 | 5.6 | 9 |
| Part-time employees | 45 | 7.0 | 4 |
(a) Test, at the 5% level of significance, the manager’s claim. You should state your hypotheses, test statistic, critical value and conclusion clearly.
(b) State two assumptions you have made in carrying out the test in part (a)
The company increases the size of the sample of part-time employees to 46 The time taken to complete the task by the extra employee is 8 minutes.
(c) Find an unbiased estimate of the variance for the sample of 46 part-time employees.
题目中文翻译
一家大公司的经理正在调查公司员工完成一项任务所需的时间。
经理认为，全职员工完成该任务的平均时间比兼职员工完成该任务的平均时间快超过 1 分钟。
经理随机抽取了 605 名全职员工和 45 名兼职员工，并记录每位员工完成该任务所用的时间 t 分钟。 结果汇总如下表。
| n | t | s^2 | |
|---|---|---|---|
| 全职员工 | 605 | 5.6 | 9 |
| 兼职员工 | 45 | 7.0 | 4 |
(a) 在 5% 显著性水平下检验经理的说法。 你应清楚写出原假设、检验统计量、临界值和结论。
(b) 写出在完成 (a) 小题的检验时所作的两个假设。
公司将兼职员工的样本量增加到 46。 新增的那位员工完成任务所用时间为 8 分钟。
(c) 求 46 名兼职员工样本的无偏方差估计。