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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Spring 2020 • Question 9

Question

Math 6010 • Linear Models Spring 2020 • Question 9

Suppose a box contains 6 marbles in total. Suppose \(\theta \) of them are white and \(6-\theta \) of them are black. Test \(H_0:\theta =2\) against \(H_a:\theta \ne 2\) as follows: draw two marbles without replacement and reject \(H_0\) if both marbles are the same color, otherwise do not reject. What is the probability of Type II error for each of the alternatives \(\theta =1\) and \(\theta =3\)?

Raw LaTeX

Suppose a box contains 6 marbles in total. Suppose \(\theta\) of them
are white and \(6-\theta\) of them are black. Test \(H_0:\theta=2\) against
\(H_a:\theta\ne 2\) as follows: draw two marbles without replacement and reject
\(H_0\) if both marbles are the same color, otherwise do not reject. What is the
probability of Type II error for each of the alternatives \(\theta=1\) and
\(\theta=3\)?

Topic Tags

Classical Probability and Inclusion-Exclusion Convergence in Probability and Almost Sure Convergence F-Tests and t-Tests Uniform Integrability and Truncation Methods