A national health survey collected the following data on self-perceived health status. The goal is to compare the proportion of people who believe they are in good health across regions of the United States.

Personal Health Assessment

Good Health Bad Health

Northeast 954 78

Region Midwest 377 160

South 459 204

West 985 87

a. Write the null and alternative hypothesis. Carry out the hypothesis test and report your results and conclusion at significance level =0.05.

b. Construct and interpret a 95% confidence interval for the odds ratio comparing the West to the South. Which region has higher odds of believing they have good health?

c. Consider only the West region and suppose that we have just completed a prospective study in which a cohort of people was monitored for 2 years. We ascertain the self-perceived health status of each cohort member at the beginning of the study and then again 2 years later. What statistical procedure would you use to test whether the current proportion of people who believe they are in good health is different from what it was 2 years ago in the West?