Suppose that x = 261 is an observation from a B(302, pA) random variable, and that y = 401 is an observation from a B(454, pB) random variable.
(a) Compute a two-sided 99% confidence interval for PA - PB
(b) Compute a two-sided 90% confidence interval for PA - PB
(c) Compute a one-sided 95% confidence interval that provides an upper bound for pA - pB.
(d) Calculate the p-value for the test of the hypotheses
H0: pA = PB versus HA: pA ≠ pB