Suppose that (X1, Y1), . . . , (Xn, Yn) are i.i.d. pairs of random variables with

Question:

Suppose that (X1, Y1), . . . , (Xn, Yn) are i.i.d. pairs of random variables with a continuous joint distribution. Let p = Pr(Xi ≤ Yi), and suppose that we want to test the hypotheses
H0: p ≤ 1/2,
H1: p > 1/2. (10.8.7)
Describe a version of the sign test to use for testing these hypotheses.