Takahe birds are native to New Zealand and are very rare. The male birds and female birds look very similar. The only way of differentiating males from females is to measure their weights. It is known that the female bird is slightly smaller than the male, and so weighing them could be a way of identifying the gender of an adult Takahe bird.

The weights of ten male and eight female Takahe birds are measured, and the summative statistics are presented in the following table.

a. Find s²_p, the pooled estimator of the population variance.

b. Test, at the 5% significance level, whether male Takahe birds are heavier than female Takahe birds assuming the weights are normally distributed.

Transcribed Image Text:

Sample size Sum Sum of squares Male 10 28.1 79.4 Female 8 21.5 58.3