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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2008 • Question 9

Question

Math 6010 • Linear Models Fall 2008 • Question 9

Let \(X_1,\ldots ,X_N\) be independent random variables. The distibution of \(X_i\) is binomial \((n_i,p_i)\). We wish to test \(H_0:p_1=p_2=\cdots =p_N\) against the alternative that \(H_0\) is not true.

a. Derive the likelihood ratio test. (5 points)

b. Provide a large sample approximation for the rejection region. (2 points)

Raw LaTeX

Let \(X_1,\ldots,X_N\) be independent random variables. The
distibution of \(X_i\) is binomial \((n_i,p_i)\). We wish to test
\(H_0:p_1=p_2=\cdots=p_N\) against the alternative that \(H_0\) is not true.

a. Derive the likelihood ratio test. (5 points)

b. Provide a large sample approximation for the rejection region. (2 points)

Topic Tags

Covariance and Independence F-Tests and t-Tests Likelihood Ratio Tests Maximum Likelihood Estimation