5. The times, \(x\) seconds, taken by the competitors in the 100 m freestyle events at a school swimming gala are recorded. The following statistics are obtained from the data.
| No. of competitors | Sample Mean \(\bar { x }\) | \(\sum x ^ { 2 }\) |
| Girls | 8 | 83.10 | 55746 |
| Boys | 7 | 88.90 | 56130 |
Following the gala a proud parent claims that girls are faster swimmers than boys. Assuming that the times taken by the competitors are two independent random samples from normal distributions,
- test, at the \(10 \%\) level of significance, whether or not the variances of the two distributions are the same. State your hypotheses clearly.
- Stating your hypotheses clearly, test the parent's claim. Use a \(5 \%\) level of significance.