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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2009 • Question 7

Question

Math 6010 • Linear Models Spring 2009 • Question 7

Let \(X_1,\ldots ,X_n\) be a random sample from \(\operatorname {Uniform}[0,\theta ]\). Find the UMP test of size \(\alpha \) of \(H_0:\theta \geq \theta _0\) vs. \(H_a:\theta <\theta _0\) by first deriving a most powerful test of simple hypotheses and then extending it to composite hypotheses.

Raw LaTeX

Let \(X_1,\ldots,X_n\) be a random sample from \(\UNIF[0,\theta]\).
Find the UMP test of size \(\alpha\) of \(H_0:\theta\geq\theta_0\) vs.
\(H_a:\theta<\theta_0\) by first deriving a most powerful test of simple
hypotheses and then extending it to composite hypotheses.

Topic Tags

F-Tests and t-Tests General Linear Hypotheses Uniform Integrability and Truncation Methods