2a) Some have argued that the F test for equality of variances should be used to decide whether to use the pooled t-test or the non-pooled t-test. Others have argued that the variances should never be assumed to be exactly equal, and the non-pooled t-test should always be used. You will explore this here via simulation. We will consider testing the following hypotheses (using either a pooled or a non-pooled t-test) at the 5% level. Ho: H1 - H2_= 0 H1: H1 - H2 # 0 Assume that we take independent simple random samples of size 20 from each of two populations. The populations are N(0,12) and a N(u,52). Use a simulation-based method to plot the power curves for the pooled and non-pooled t-tests (on the same graph) as a function of a sequence of u values from -5 to 5. Use the following R code to plot the power functions (based on simulation) for this test when conditioning on the true difference in means. mu vals