- 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.
| \(n\) | \(\bar { t }\) | \(s ^ { 2 }\) |
| Full-time employees | 605 | 5.6 | 9 |
| Part-time employees | 45 | 7.0 | 4 |
- Test, at the \(5 \%\) level of significance, the manager's claim.
You should state your hypotheses, test statistic, critical value and conclusion clearly.
- 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.
- Find an unbiased estimate of the variance for the sample of 46 part-time employees.