- A teacher wishes to test whether playing background music enables students to complete a task more quickly. The same task was completed by 15 students, divided at random into two groups. The first group had background music playing during the task and the second group had no background music playing.
The times taken, in minutes, to complete the task are summarised below.
| Sample size \(n\) | Standard deviation \(s\) | Mean \(\bar { x }\) |
| With background music | 8 | 4.1 | 15.9 |
| Without background music | 7 | 5.2 | 17.9 |
You may assume that the times taken to complete the task by the students are two independent random samples from normal distributions.
- Stating your hypotheses clearly, test, at the \(10 \%\) level of significance, whether or not the variances of the times taken to complete the task with and without background music are equal.
- Find a 99\% confidence interval for the difference in the mean times taken to complete the task with and without background music.
Experiments like this are often performed using the same people in each group.
- Explain why this would not be appropriate in this case.