Refer to Exercise 10.113. Suppose that another independent

Chapter 10, Problem 114E

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Problem 114E

Refer to Exercise 10.113. Suppose that another independent random sample of size n3 is selected from a third normal population with mean μ3 and variance σ 2. Find the likelihood ratio test for testing H0 : μ1 = μ2 = μ3 versus the alternative that there is at least one inequality. Show that this test is equivalent to an exact F test.

Reference

Refer to Exercise 10.112. Show that in testing of H0 : μ1 = μ2 versus Ha : μ1 ≠ μ2 (σ 2 unknown) the likelihood ratio test reduces to the two-sample t test.

Suppose that independent random samples of sizes n1 and n2 are to be selected from normal populations with means μ1 and μ2, respectively, and common variance σ 2. For testing H0 : μ1 = μ2 versus Ha : μ1 − μ2 > 0 (σ 2 unknown), show that the likelihood ratio test reduces to the two-sample t test presented in Section 10.8.