题目
Problem
A manager is investigating the times taken by employees to complete a particular task as a result of the introduction of new technology. He claims that the mean time taken to complete the task is reduced by more than 0.4 minutes. He chooses a random sample of 10 employees. The times taken, in minutes, before and after the introduction of the new technology are recorded in the table.
| Employee | A | B | C | D | E | F | G | H | I | J |
|---|---|---|---|---|---|---|---|---|---|---|
| Time before new technology | 10.2 | 9.8 | 12.4 | 11.6 | 10.8 | 11.2 | 14.6 | 10.6 | 12.3 | 11.0 |
| Time after new technology | 9.6 | 8.5 | 12.4 | 10.9 | 10.2 | 10.6 | 12.8 | 10.8 | 12.5 | 10.6 |
(a) Test at the 10% significance level whether the manager’s claim is justified.
[7]
(b) State an assumption that is necessary for this test to be valid.
[1]
题目中文翻译
一名经理正在研究引入新技术后，员工完成某项特定任务所需时间的情况。他声称，完成该任务所需的平均时间减少了超过 0.4 分钟。他随机抽取 10 名员工。引入新技术前后所需的时间（单位：分钟）记录在表中。
| 员工 | A | B | C | D | E | F | G | H | I | J |
|---|---|---|---|---|---|---|---|---|---|---|
| 新技术前用时 | 10.2 | 9.8 | 12.4 | 11.6 | 10.8 | 11.2 | 14.6 | 10.6 | 12.3 | 11.0 |
| 新技术后用时 | 9.6 | 8.5 | 12.4 | 10.9 | 10.2 | 10.6 | 12.8 | 10.8 | 12.5 | 10.6 |
(a) 在 10% 显著性水平下，检验这名经理的声称是否成立。
(b) 说明该检验有效所需的一个假设。