A study used 1259 patients who had suffered a stroke. The study randomly assigned each subject to an aspirin treatment or a placebo treatment. During a 3-year follow-up period, in Sample 1, 634 people received placebo treatments and 25 people died from heart attack. In sample 2, 625 people received aspirin treatment and 18 died from heart attack.
Let p1 denote the population proportion of death from heart attack for those received placebo and p2 denote the population proportion of death from heart attack for those received aspirin treatment.
(a) What is the sampling distribution of ˆp1 − ˆp2? State the assumptions which the sampling distribution is based.
(b) Matching problem: Assuming that the two population proportions are the same, let SE0 denote the standard error of ˆp1 − ˆp2. Without this assumption, the standard error is denoted SE1. Select SE0 and SE1 from the following.

i) √ [ ([^p1 (1 - ^p1)]/n1) + ([^p2 (1 - ^p2)]/n2) ]= 1.0401
ii) √([^p (1 - ^p)]([1/n1]+[1/n2])) = 1.0206 where ^p = (25 + 18) / (634 + 625)

(c) Which of SE0 and SE1 is used for calculating a confidence interval for comparing two population proportions? Which is used for calculating the test statistic in a hypothesis test?
(d) Construct the 95% confidence interval for p1 − p2. Interpret.
(e) If we instead let sample 1 refer to the aspirin treatment and sample 2 the placebo treatment, explain how the point estimate of the difference and the 95% confidence interval would change. Explain how then to interpret the confidence interval.
(f) In general, does a conclusion from a two-tailed two-sample z-test for proportions (with the significance level = α) agree with the 100(1-α)% confidence interval for p1 − p2? Why or why not? (You DO NOT need to do a hypotheses testing).