Let X1…X5 be iid random sample of size n=5 from a Uniform distribution with parameters 0,theta....

Let X1…X5 be iid random sample of size n=5 from a Uniform distribution with parameters 0,theta. We test H0: theta=1 versus H1: theta=2. Reject H0 when max(X1…X5)>b.

Find the value of b so that the size of the test is 0.10, then find the power of this test.
Among the tests based on max(X1…Xn), find the most powerful test with size exactly equal to 0.

Solutions

Expert Solution

For this question you need concepts of hypothesis testing.

Neyman - Pearson Lemma to obtain most powerful test. Also you must know how to obtain likelihood in case of order statistics.

I have solved the question with proper steps.

orchestra answered 1 year ago

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