Bombardier beetles Pheropsophus jessoensis eject a hot chemical spray from the tip of their abdomens when attacked. Does this sometimes improve their survival? As part of a study to test this possibility, Sugiura and Sato (2018) presented a single beetle to each of 23 toads, Bufo japonicus. All toads ate the beetle, after which “an explosion was audible inside each toad,” indicating that each beetle had discharged. Eight of the toads vomited up the beetles, each of which then survived the ordeal. The other 15 beetles were not vomited up and were digested instead.

a. From these data, what is the best estimate of the proportion of beetles that survive ingestion by Bufo japonicus?

b. What is the 95% confidence interval for the proportion of beetles in the population who survive ingestion by Bufo japonicus?

c. What is the best estimate from these data of the proportion of beetles that fail to survive?