84. Assume that X is uniformly distributed on (1, 1)

and Y is split evenly between a uniform distribution on (101, 100) and a uniform distribution on

(100, 101). Thus the means are both 0, but the variances differ strongly. We take random samples of three from each distribution and apply a permutation test for the null hypothesis H0: m1  m2 against the alternative Ha: m1  m2.

a. Show that the probability is that all three of the Y values come from (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 con ict. What is the true probability that the permutation test rejects the null hypothesis at the .05 level?