A clinical trial is planned to compare drugs A and B for lowering cholesterol levels. Partic- ipants will be randomized in a 1:1 ratio to each of the two arms. Cholesterol levels will be recorded at months 3, 6 and 9 following randomization for each participant. Let A and B be the mean cholesterol levels in each of the arms, and suppose that the standard deviation of one cholesterol measurement is = 40 mg/dL and that the correlation between any two cholesterol measurements from the same subject is = 0.20. The study must detect a mean difference of 10mg/dL with 90% power at significance level 0.05. (a) If the study will test H0 : A = B vs H1 : A 6= B where A and B are the population mean cholesterol levels after 9 months of treatment for each of the drugs, how many subjects are needed in each arm? Include the unfortunate fact that we expect 10% of the subjects to drop out and so will not be able to provide a measurement at 9 months. (b) Some investigators advocate for randomizing twice as many subjects to A as to B because the drug B is considerably more expensive than A. If the allocation ratio is changed to 2:1 (A:B), how many subjects are needed in each arm to test the hypotheses for the mean cholesterol levels at 9 months (continuing to allow for 10% drop out)? (c) Returning to the 1:1 allocation, investigators think that it takes only about 2 months for these drugs to work, and that the drugs will have no additional effect after 2 months of treatment. So another analysis approach will average the 3, 6 and 9 month measurements for each subject, and then average these averages within each arm to estimate the mean cholesterol level for the arm. Again testing H0 : A = B vs H1 : A 6= B, how many subjects are needed in each arm? Again include the anticipated drop out of 10%

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PLEASE EXPLAIN HOW TO SOLVE C.