For all sample size calculation, alpha = 0.05 (i.e the confidence level =95%), and the power is 80% (i.e. beta = 0.2).

Question 1 part A We are going to study the difference in means of two paired samples. We assume the difference in mean between these two samples (mu_d) is 4, and the standard deviation of this difference is 16. Our hypothesis is H0: mu_d = 0 vs Ha: mu_d not equal to 0. To achieve a power of 80% to test the difference of 4, how many patients in each group should we recruit? The significance level is 0.05, and we assume attrition = 20%.

Question 1 part B: We are going to study the difference in means of two independent samples. We assume the difference in mean between these two samples is 5.0 (assuming: mu1=16 and mu2=11), and the standard deviation (among all patients in two groups) is 20. Our hypothesis is H0: mu1 = mu2 vs Ha: mu1 not equal to mu2. To achieve a power of 80% to test the difference of 5.0, how many patients in total should we recruit? The significance level is 0.05, and we assume attrition = 10%.