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Suppose that independent random samples of sizes n1 and n2
Chapter 10, Problem 112E(choose chapter or problem)
Problem 112E
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.
Questions & Answers
QUESTION:
Problem 112E
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.
ANSWER:
Step 1 of 7
We have from Normal distribution with mean and variance and from Normal distribution with mean and variance . We have to find likelihood ratio test for