You conduct a study on the effect of type of defense counsel on the outcome of a criminal trial. You have the information from a random sample of 20 criminal trials on the outcome of the trial (0 = acquitted, 1 = convicted) and type of defense counsel (0 = private, 1 = public defender). With these data, you run a logistic regression analysis with the outcome of the trial as the dependent variable and the type of defense counsel as the independent variable. Here are the results of that logistic regression:
Using this output, answer the following questions:
a. Write the full logistic regression equation.
b. Interpret the regression coefficient.
c. Test the null hypothesis that the logistic regression coefficient for COUNSEL in the population is zero against the alternative that it is different from zero. Use an alpha of 0.05.
d. Compute the probabilities of a conviction for both defendants with private counsel and defendants with public defenders. What are their respective odds of a conviction?
See attached file for full problem description.
Word document attached helps test hypotheses, write logistic regression equations and interpret a regression coefficient among other related things.