Suppose that X1, , Xn form a random sample from the uniform distribution described in Exercise 6, but suppose now that it is desired to test the following hypotheses H0 3, H1 3 a Show that at each level of significance 0 (0 0 1), there exists a UMP test that specifies that H0 should be rejected if max X1, , Xn c b Determine the value of c for each possible value of 0

Question: Suppose that X1, . . . , Xn form a random sample from the uniform distribution described in Exercise 6, but suppose now that it

Suppose that X1, . . . , Xn form a random sample from the uniform described in Exercise 6, but suppose now that it is desired to test the following hypotheses:
H0: θ ≥ 3,
H1: θ <3.
a. Show that at each level of significance α0 (0 < α0 < 1), there exists a UMP test that specifies that H0 should be rejected if max{X1, . . . , Xn} ≤ c.
b. Determine the value of c for each possible value of α0.

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