Refer to Exercise 10.5. Find the power of test 1 for each alternative in (a)–(e).
a θ = .1.
b θ = .4.
c θ = .7.
d θ = 1.
e Sketch a graph of the power function.
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).]
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