Suppose we will run an experiment that compares three treatments: A, B, and C. The shared variance could be 2 = 1. Consider the model yij = j + eij where eij N(0, 2 ). Here j = 1, 2, 3, for A, B, and C. The null hypothesis of the test we will run is: H0 : A = B = C Suppose that we're interested in an alternative where A = 1, B = 0, C = 1 Mostly, we've used simulation to verify results. Now, we'll use simulation to save money (in place of some rather difficult mathematics)! Use simulation to determine the minimum sample size that has at least a 90% chance to reject the null hypothesis when that alternative is true and = 0.05. That is, find the sample size which gives a power of at least 0.90 for the stated alternative. Consider only balanced designs, which have the same number of replications in each group. For each sample size, use at least 250 simulations. (More simulations will give a better estimate of the power and will create smoother resulting curve.) Plot your results. What sample size do you choose? Before performing the simulations, set a seed value equal to your birthday, as was done in the previous homework assignments.

Using R

birthday = 18760613 set.seed(birthday)