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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2009 • Question 8

Question

Math 6010 • Linear Models Spring 2009 • Question 8

Let \(X_1,\ldots ,X_n\) be a random sample from \(N(\mu ,\sigma _0^2)\), where \(\sigma _0^2\) is known. Find the generalized likelihood ratio test of size \(\alpha \) of \(H_0:\mu \geq \mu _0\) vs. \(H_a:\mu <\mu _0\).

Raw LaTeX

Let \(X_1,\ldots,X_n\) be a random sample from \(\N(\mu,\sigma_0^2)\),
where \(\sigma_0^2\) is known. Find the generalized likelihood ratio test of size
\(\alpha\) of \(H_0:\mu\geq\mu_0\) vs. \(H_a:\mu<\mu_0\).

Topic Tags

F-Tests and t-Tests Likelihood Ratio Tests Maximum Likelihood Estimation Uniform Integrability and Truncation Methods