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

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%.