Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6010 • Linear Models

Fall 2016 • Question 10

Question

Math 6010 • Linear Models Fall 2016 • Question 10

Suppose that an engineer wishes to compare the number of complaints per week filed by union stewards for two different shifts at a manufacturing plant. It is known that the number of complaints per week on the \(i\)th shift has a Poisson distribution with mean \(\theta _i\) for \(i=1,2\). One hundred independent observations on the number of complaints gave means \(\bar x=20\) for shift 1 and \(\bar y=22\) for shift 2. Using this data test \(H_0:\theta _1=\theta _2\) versus \(H_1:\theta _1\ne \theta _2\) by the likelihood ratio method, with \(\alpha =0.01\). (Hint: First find the likelihood ratio test statistic for \(\lambda \) and then use the distribution of \(-2\log \lambda \).)

Suppose that an engineer wishes to compare the number of complaints
per week filed by union stewards for two different shifts at a manufacturing
plant. It is known that the number of complaints per week on the \(i\)th shift
has a Poisson distribution with mean \(\theta_i\) for \(i=1,2\). One hundred
independent observations on the number of complaints gave means \(\bar x=20\) for
shift 1 and \(\bar y=22\) for shift 2. Using this data test \(H_0:\theta_1=\theta_2\)
versus \(H_1:\theta_1\ne\theta_2\) by the likelihood ratio method, with
\(\alpha=0.01\). (\textbf{Hint:} First find the likelihood ratio test statistic
for \(\lambda\) and then use the distribution of \(-2\log\lambda\).)

Topic Tags

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