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 with no treatment and p2 denote the population proportion of death from heart attack for those with aspirin treatment. (a). What is the sampling distribution of ˆp1−ˆp2? State the assumptions on which the sampling distribution is based.
(b). Assuming that the two population proportions are the same, letSE0denote the standard error of ˆp1−ˆp2. Without this assumption, the standard error is denoted SE1. Find SE0 and SE1.
(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.