In a phase III clinical trial, we would like to compare a new treatment with equal allocation. Let 1 and 0 be the population response rates for the treatment and the control group, respectively. We want to test H0 : 1 0 = 0 vs. HA : 1 0 = 0 at a level = 0.05. We assume that we would like to have power 0.9 to detect 0 = 0.8 and 1 = 0.9. (a) If you were to use the proportions test to test for significance, based on the design considerations above, what sample size would you recommend? Please show all your calculations. (b) If you were to use the test based on the arc sine square root transformation to test for significance, based on the design considerations above, what sample size would you recommend? Please show all your calculations. (c) Please describe the type I error and type II error