Let x1 , x2 be iid uniform(θ,θ+1), θ ≥ 0, and consider the test h0: θ = 0 against h1: θ > 0.

suppose we have two competing tests:
test 1: reject the null if x1 > .95.
test 2: reject the null if x1 + x2 > c, where c is a constant specified by the researcher.
a. find the value of c such that the two tests have equal size.
b. define the power function for each test (the second will be piecewise). draw (or use software to create) a graph of the power function for each test.