Question 3. Suppose we have two samples, X1, . , Xm and Y1, . , Yn. Consider rejecting for a large value of a test statistic U = h(X1, . , Xm, Y1, ....

Question 3. Suppose we have two samples, X1, . . . , Xm and Y1, . . . , Yn. Consider rejecting for a large value of a test statistic U = h(X1, . . . , Xm, Y1, . . . , Yn). Describe precisely (and concisely) how you would obtain the corresponding permutation p-value.

Question 4.(continued from Question 3) Describe a generic rank-based test in this situation. [Make sure to say how the ranks are computed.] Name a couple of such tests.

Question 5. (continued from Questions 3-4) What is the null hypothesis that is being tested? [Hint: Under what null hypothesis is the permutation p-value valid?