In the study for cancer death rates, consider the null hypothesis that the population proportion of cancer deaths p1 for placebo is the same as the population proportion p2 for aspirin. The sample proportions were p̂1 = 347/11,535 = 0.030 and p̂2 = 327/14,035 = 0.023.
a. For testing H0: p1 = p2 against Ha: p1 = p2, show that the pooled estimate of the common value p under H0 is p̂ = 0.027 and the standard error is 0.002.
b. Show that the test statistic is z = 3.5.
c. Find and interpret the P-value in context.