Assume that X is uniformly distributed on [−1, 1] and the Y distribution is uniform on the two intervals [–101, –100] and [100, 101]. Thus the means are both 0, but the variances differ substantially. We take random samples of size three from each distribution and apply a permutation test for the null hypothesis H₀: μ₁ = μ₂ against the alternative H_a: μ₁ < μ₂.

a. Show that the probability is 1/8 that all three of the Y values come from the interval [100, 101].
b. Show that, if all three Y values come from [100, 101], then the P-value for the permutation test is .05.
c. Explain why (a) and (b) are in conflict. What is the probability that the permutation test rejects the null hypothesis at the .05 level?