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, 0 and 9 following randomization for each participant. Let a}; and p.15 be the mean cholesterol levels in each of the arms, and suppose that the standard deviatior of one cholesterol measurement is 0' = 40 mg/dL and that the correlation between any twr cholesterol measurements from the same subject is p = 0.20. The study must detect a meat difference of 10mg/dL with 90% power at signicance level 0.05. (a) (b) If the study will test Ho : HA : #3 vs H1 : p.31, 75 of; where ILA and pg 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 expeci 10% of the subjects to drop out and so will not be able to provide a measurement at E months. 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 tc 2:1 (AB), 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)? Returning to the 1:1 allocation, investigators think that it takes only about 2 months f0] these drugs to work, and that the drugs will have no additional effect after 2 months o1 treatment. So another analysis approach will average the 3, 5 and 9 month measurement: for each subject, and then average these averages within each arm to estimate the mear cholesterol level for the arm. Again testing Ho : pg 2 p3 vs H1 : pg # o5, how many subjects are needed in each arm? Again include the anticipated drop out of 10%