5. (9 points) (Pagano/Gauvreaux Ch15 Q12) Suppose you are interested in investigating the factors that affect the prevalence of tuberculosis among intravenous drug users. In a group of 97 individuals who admit to sharing needles, 24.7% had a positive tuberculin skin test result; among 161 drug users who deny sharing needles, 17.4% had a positive test result.

a. Assuming that the population proportions of positive skin test results are in fact equal, estimate the pooled success proportion.

b. Test the null hypothesis that the proportions of intravenous drug users who have a positive tuberculin skin test result are identical for those who share needles and those who do not.

c. Construct a 95% confidence interval for the true difference in proportions.