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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2016 • Question 1

Question

Math 6010 • Linear Models Spring 2016 • Question 1

Let \(X_1,\ldots ,X_n\) be a random sample with density function \(f(x)=2e^{-2(x-\eta )}\) for \(x>\eta \), and zero otherwise. We wish to test \(H_0:\eta =4\) versus the alternative \(H_A:\eta >4\). We reject \(H_0\) if \(X_{(1)}=\min _{1\leq i\leq n}X_i\geq 4+2/n\).

(a) Compute the significance level of the test.

(b) Compute the power function.

Raw LaTeX

Let \(X_1,\ldots,X_n\) be a random sample with density function
\(f(x)=2e^{-2(x-\eta)}\) for \(x>\eta\), and zero otherwise. We wish to test
\(H_0:\eta=4\) versus the alternative \(H_A:\eta>4\). We reject \(H_0\) if
\(X_{(1)}=\min_{1\leq i\leq n}X_i\geq 4+2/n\).

\textbf{(a)} Compute the significance level of the test.

\textbf{(b)} Compute the power function.

Topic Tags

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