Refer to Exercise 10.5.a Find the power of test 2 for each

Chapter 10, Problem 90E

(choose chapter or problem)

Problem 90E

Refer to Exercise 10.5.

a Find the power of test 2 for each of the following alternatives: θ = .1, θ = .4, θ = .7, and θ = 1.

b Sketch a graph of the power function.

c Compare the power function in part (b) with the power function that you found in Exercise 10.89 (this is the power function for test 1, Exercise 10.5). What can you conclude about the power of test 2 compared to the power of test 1 for all θ ≥ 0?

Reference

Let Y1 and Y2 be independent and identically distributed with a uniform distribution over the interval (θ, θ + 1). For testing H0 : θ = 0 versus Ha :θ > 0, we have two competing tests:

Test 1: Reject H0 if Y1 > .95.

Test 2: Reject H0 if Y1 + Y2 > c.

Find the value of c so that test 2 has the same value for α as test 1. [Hint: In Example 6.3, we derived the density and distribution function of the sum of two independent random variables that are uniformly distributed on the interval (0, 1).]