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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2015 • Question 4

Question

Math 6010 • Linear Models Fall 2015 • Question 4

Let \(X_1,X_2,\ldots ,X_n\) be independent, identically distributed random variables with density function \[ h(t;\mu )=\frac {1}{(2\pi )^{1/2}}e^{-(t-\mu )^2/2}. \] We wish to test \(H_0:\mu \leq \mu _0\) against \(H_A:\mu >\mu _0\). Find the uniformly most powerful test of size \(\alpha \).

Raw LaTeX

Let \(X_1,X_2,\ldots,X_n\) be independent, identically distributed
random variables with density function
\[
h(t;\mu)=\frac{1}{(2\pi)^{1/2}}e^{-(t-\mu)^2/2}.
\]
We wish to test \(H_0:\mu\leq\mu_0\) against \(H_A:\mu>\mu_0\). Find the uniformly
most powerful test of size \(\alpha\).

Topic Tags

Covariance and Independence F-Tests and t-Tests Measure-Theoretic Probability Uniform Integrability and Truncation Methods