In 2002 the Supreme Court ruled that schools could require random drug tests of students participating in competitive after-school activities such as athletics. Does drug testing reduce use of illegal drugs? A study compared two similar high schools in Oregon. Wahtonka High School tested athletes at random and Warrenton High School did not. In a confidential survey, 7 of 135 athletes at Wahtonka and 27 of 141 athletes at Warrenton said they were using drugs. Regard these athletes as SRSs from the proportions of athletes at similar schools with and without drug testing.
(a) You should not use the large sample confidence interval. Why not?
(b) The plus four method adds two observations, a success and a failure, to each sample. What are the sample sizes and the numbers of drug users after you do this?
(c) Give the plus four 95% confidence interval for the difference between the proportion of athletes using drugs at schools with and without testing.
This solution includes detailed answers for each question. Provided is a detailed explanation of finding the plus four confidence interval for the difference between two population proportions.