Which approach to compare two independent groups is best under different assumed distributions? Specifically, we'd like to explore how the following 4 approaches behave under varying underlying distributions: 1. 2-sample f-test. 2. 2-sample f-test on the log scale. 3. Wilcoxon rank sum test. 4. Permutation test (based on 1000 resamplings each time) Perform a simulation (with nsims = 1000) to estimate the probability of rejecting the null hypothesis for each of the tests mentioned above under the conditions stated below. (a) Let X, ~ N(20. 32 ) and Y, ~ N (20,3?) (all observations independent). Report the estimated rejection rate for each of the 4 tests when n = 10 in each group and separately when n = 100 in each group. Print out the histogram of p-values for each of the 4 tests (b) Let X, ~ N(20, 3') and Y, ~ N(21,3') (all observations independent). Report the estimated rejection rate for each of the 4 tests when n = 10 in each group and separately when n = 100 in each group. (c) Let log(X,) ~ N(0, 1) and log(Y) ~ N(0, 1) (all observations independent). Report the estimated rejection rate for each of the 4 tests when n = 10 in each group and separately when n = 100 in each group. (d) Let In(X) ~ N(0, 1) and In(Y) ~ N(0.5, 1) (all observations independent). Report the estimated rejection rate for each of the 4 tests when n = 10 in each group and separately when n = 100 in each group. (e) Interpret the results of the simulations above. Which test is most robust to the conditions considered? Which test is properly most powerful? If you had no idea what distribution your data would be sampled from, which test would you choose