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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2016 • Question 6

Question

Math 6010 • Linear Models Fall 2016 • Question 6

Let \(X_1,X_2,\ldots ,X_{25}\) denote a random sample of size 25 from a normal distribution with mean \(\theta \) and variance 100. Find a uniformly most powerful critical region of size \(\alpha =0.10\) for testing \(H_0:\theta =75\) against \(H_1:\theta >75\).

Raw LaTeX

Let \(X_1,X_2,\ldots,X_{25}\) denote a random sample of size 25 from a
normal distribution with mean \(\theta\) and variance 100. Find a uniformly most
powerful critical region of size \(\alpha=0.10\) for testing \(H_0:\theta=75\)
against \(H_1:\theta>75\).

Topic Tags

Analysis of Variance Estimator Distributions Multivariate Normal Distributions Uniform Integrability and Truncation Methods