Suppose we are planning a clinical trial and expect a 20% success rate in the active group and a 10% success rate in the placebo group. We expect to enrol 100 participants in each group and are interested in the power of the study. (a) Perform a simulation study, and generate 100 participants from a binomial distribution with p = 0:2 and 100 participants from a binomial distribution with p = 0:1. Test to find out whether the observed sample proportion of successes is significantly different, using a two-sided test with α = 0:05. (b) Repeat the Problem (a) simulation 100 times, and compute the proportion of simulations in which a significant difference is found (i.e., an estimate of the power of the study). (c) What should the theoretical power be for the exercise in Problem (b)? How do the estimated power and theoretical power compare?