5. Fire brigades in cities \(X\) and \(Y\) are in similar locations. The response times, in minutes, during a particular month, for randomly selected calls are summarised in the table below.
| \cline { 2 - 4 }
\multicolumn{1}{c|}{} | Sample size | Sample mean | |
| \(X\) | 9 | 14.8 | 6.76 |
| \(Y\) | 6 | 7.2 | 5.42 |
You may assume that the response times are from independent normal distributions.
Stating your hypotheses and showing your working clearly
- test, at the \(10 \%\) level of significance, whether or not the variances of the populations from which the response times are drawn are the same,
(5) - test, at the \(5 \%\) level of significance, whether or not the mean response time for the fire brigade in city \(X\) is more than 5 minutes longer than the mean response time for the fire brigade in city \(Y\).
- Explain why your result in part (a) enables you to carry out the test in part (b).