Suppose that X1, , Xn form a random sample from the uniform distribution on the interval 0, , and that the following hypotheses are to be tested H0 2, H1 2 Let Yn max X1, , Xn , and consider a test procedure such that the critical region contains all the outcomes for which Yn 1 5 a Determine the po...

a We know that if 0 y then PrY n y y n Al ...

Suppose that X1, . . . , Xn form a random sample from the uniform distribution on

Question:

Suppose that X1, . . . , Xn form a random sample from the uniform on the interval [0, θ], and that the following hypotheses are to be tested:
H0: θ ≥ 2,
H1: θ <2.
Let Yn = max{X1, . . . , Xn}, and consider a test procedure such that the critical region contains all the outcomes for which Yn ≤ 1.5.
a. Determine the power function of the test.
b. Determine the size of the test.
Distribution
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