In a phase III clinical trial we would like to compare 3 new treatments to the standard treatment on lowering patients' cholesterol levels. Assume the standard deviation of patients' cholesterol levels is 25. (a) [15 points] We would like to detect whether or not patients' cholesterol levels treated with a new treatment will be 20 unit lower than those treated with the standard treatment with 90% power at a significance level 0.01. Find the necessary sample size under equal allocation assumption. The following information may be useful: 2(0.01, 0.1, 2) = 17.4, 2(0.01, 0.1, 3) = 19.2, 2(0.01, 0.1, 4) = 20.7. (b) [15 points] Suppose after the study, we got the following data on LDL (bad cholesterol): 1 Treatment 1 Treatment 2 Treatment 3 Treatment 4 Sample size (ni) 58 65 55 62 Sample mean (i) 158 160 155 140 Suppose the pooled sample variance is 900. One would like to test if all treatments will yield the same mean of cholesterol levels (i.e., H0 : 1 = 2 = 3 = 4) at the significance level 0.05 assuming equal variance. What is the distribution of the test statistic under H0? What is the conclusion one will get? The