In the garden spider Araneus diadematus, the female often attempts to eat the male before or after mating, making sex a daunting prospect for the males. (This seemingly bizarre behavior, called sexual cannibalism, is not uncommon in the animal world.) In a series of mating observations, the courting male was captured and eaten by the female in 21 of 52 independent mating trials (Elgar and Nash 1988).

a. Based on the sample, estimate the proportion of males that are eaten by females, and give a 95% confidence interval for this estimate.

b. Is this estimate and confidence interval consistent with a true proportion of 50% capture of males? Is it consistent with 10% capture?

c. If the sample were much larger and the data showed instead that 210 out of 520 matings involved sexual cannibalism, would this change the estimated proportion?

d. Would the increase in sample size in part (c) change the confidence interval? How? (You don’t need to do the calculations—just answer qualitatively.)