Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2016 • Question 11

Question

Math 6010 • Linear Models Spring 2016 • Question 11

Let \(X_1,\ldots ,X_n\) be a random sample from the \(N(\theta ,1)\) distribution, \(\theta \) unknown. We wish to test \(H_0:\theta =\theta _0\) versus \(H_A:\theta <\theta _0\). Find a test using the generalized likelihood ratio \(\lambda \).

Raw LaTeX

Let \(X_1,\ldots,X_n\) be a random sample from the \(\N(\theta,1)\)
distribution, \(\theta\) unknown. We wish to test \(H_0:\theta=\theta_0\) versus
\(H_A:\theta<\theta_0\). Find a test using the generalized likelihood ratio
\(\lambda\).

Topic Tags

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