In a field study of mating behaviour in the Mormon cricket, a biologist noted that some females mated successfully while others were rejected by the males before coupling was complete. The question arose whether some aspect of body size might play a role in mating success. The accompanying table summarizes measurements of head width (mm) in
the two groups of females.

mean sd n
successful 8.568182 0.2491058 22
unsuccessful 8.497647 0.2738049 17

a) Compute the p-value to test that the mean head width as an effect in mating success. In other words, test that the means are different. Do we have strong evidence that the mean head width as an effect in mating success?

b) Construct a 95% ci for the difference between the mean head width of both groups.