- 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.
| \cline { 2 - 4 }
\multicolumn{1}{c|}{} | No. of competitors | Sample mean \(\overline { \boldsymbol { x } }\) | \(\sum \boldsymbol { x } ^ { \mathbf { 2 } }\) |
| Girls | 8 | 83.1 | 55746 |
| Boys | 7 | 88.9 | 56130 |
Following the gala, a mother 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 mother's claim. Use a \(5 \%\) level of significance.