3. The lengths, \(x \mathrm {~mm}\), of the forewings of a random sample of male and female adult butterflies are measured. The following statistics are obtained from the data.
| No. of butterflies | Sample mean \(\bar { x }\) | \(\sum x ^ { 2 }\) |
| Females | 7 | 50.6 | 17956.5 |
| Males | 10 | 53.2 | 28335.1 |
- Assuming the lengths of the forewings are normally distributed 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, at the \(5 \%\) level of significance, whether the mean length of the forewings of the female butterflies is less than the mean length of the forewings of the male butterflies.
(6)