A resaercher is planning to run a clinical trial to measure the effect of a treatment on a group of individuals. They will recruit n participants to receive the treatment (group 1), and n to receive a placebo (group 2), and will measure the proportion in each group that successfully recover from an illness. They plan to conduct a hypothesis test at the 5% significance level for p - p2 as the following: Ho P1 P2 = 0, Ha P P2 #0 : a. Using the most conservative method, what should the sample sizes of each group be so that the margin of error is no more than 0.098? [5 marks] b. Under your choice of sample size in part a, suppose the researcher finds that pi 0.08, p2 0.04. Conduct the planned hypothesis test. [5 marks] c. Under your choice of sample size in part a, give a 95% confidence interval for the difference in proportions. [5 marks] -