A random sample of n1 = 100 observations from one binomial population and a separate random sample of n2 = 75 observations from a second binomial population produced x1 = 33 and x2 = 27 successes respectively.
(i) At the α = 0.05 signi?cance level, test the hypothesis that the two population proportions are equal against the alternative that they are different.
(ii) Repeat (i) for the alternative hypothesis that p2 > p1.