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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

2004 • Question 2

Question

Math 6010 • Linear Models 2004 • Question 2

Let \(X_1,X_2,\ldots ,X_n\) be independent, identically distributed normal \(N(\mu ,\sigma ^2)\) random variables. We wish to test \(H_0:\mu =\mu _0\) against \(H_A:\mu \neq \mu _0\) (\(\sigma \) is unknown). Show that the t-test and the likelihood tests are equivalent.

Raw LaTeX

Let \(X_1,X_2,\ldots,X_n\) be independent, identically distributed normal \(N(\mu,\sigma^2)\) random variables. We wish to test \(H_0:\mu=\mu_0\) against \(H_A:\mu\neq\mu_0\) (\(\sigma\) is unknown). Show that the t-test and the likelihood tests are equivalent.

Topic Tags

Covariance and Independence F-Tests and t-Tests Likelihood Ratio Tests Maximum Likelihood Estimation