Let X be a single observation from a Uniform distribution with parameters 0,theta. We test H0:...

Let X be a single observation from a Uniform distribution with parameters 0,theta. We test H0: theta =1 versus H1: theta = 2. If X is greater than or equal to b, reject H0.

Find the value of b so that the size of the test is 0.10, then find the power of this test. Also, is there a most powerful test of size exactly equal to 0?

Expert Solution

orchestra answered 2 years ago

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.

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