Suppose that the abilities of two new radar systems to detect packages dropped by airplane are being compared. In a series of trials, radar system A detected the packages being dropped 35 times out of 44, while radar system B detected the packages being dropped 36 times out of 52.
(a) Construct a 99% two-sided confidence interval for the differences between the probabilities that the radar systems successfully detect dropped packages.
(b) Calculate the p-value for the test of the two-sided null hypothesis that the two radar systems are equally effective.