Consider a problem of testing hypotheses in which the

Chapter 9, Problem 19

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QUESTION:

Consider a problem of testing hypotheses in which the following hypotheses about an arbitrary parameter are to be tested: H0: 0, H1: 1. Suppose that is a test procedure of size (0 << 1) based on some vector of observations X, and let (|) denote the power function of . Show that if is unbiased, then (|) at every point 1.

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QUESTION:

Consider a problem of testing hypotheses in which the following hypotheses about an arbitrary parameter are to be tested: H0: 0, H1: 1. Suppose that is a test procedure of size (0 << 1) based on some vector of observations X, and let (|) denote the power function of . Show that if is unbiased, then (|) at every point 1.

ANSWER:

Step 1 of 2

Given data:

We are given the testing of problem-testing hypotheses in which the following hypotheses about an arbitrary parameter  are to be tested:

                                                                 

Suppose that  is a test procedure of size  based on the vector of observations

 , and power function of  is  . 

Now we have to show that  at every point  when  is unbiased.

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