, Fall 2006
On the course web page under “Laboratory Materials” is a link to a file that contains a generic Newton-Raphson algorithm. Also on the course web page under “Data” is a link to a file that contains values simulated from two gamma distributions. The file contains two columns of 50 values each. The first column should be considered data from Group 1 and the second column data from Group 2.
1. Find maximum likelihood estimates for gamma models formulated for these data, and well as the observed information matrix evaluated at these estimates.
2. Test whether the groups should be considered significantly different using a likelihood ratio test.
3. Produce graphs of the estimated distributions for the two groups.
4. Construct 95% confidence intervals for the expected values of the two groups using Wald Theory procedures.
5. Test whether the groups should be considered significantly different using a two-sample t-test (take square roots if you think it makes the data groups look more symmetric). Use either equal variance or unequal variance forms of the t-test.