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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2018 • Question 10

Question

Math 6010 • Linear Models Fall 2018 • Question 10

Let \(X_1,X_2,\ldots ,X_{25}\) denote a random sample of size 25 from a \(N(\theta ,100)\) distribution. Find a uniformly most powerful critical region of size \(\alpha =.10\) for testing \(H_0:\theta =75\) against \(H_A:\theta >75\).

Raw LaTeX

Let \(X_1,X_2,\ldots,X_{25}\) denote a random sample of size 25 from
a \(\N(\theta,100)\) distribution. Find a uniformly most powerful critical region
of size \(\alpha=.10\) for testing \(H_0:\theta=75\) against \(H_A:\theta>75\).

Topic Tags

Estimator Distributions Multivariate Normal Distributions Quadratic Forms and Chi-Squared Distributions Uniform Integrability and Truncation Methods