Question: Drug testing in schools. Does drug testing reduce use of illegal drugs by high school athletes? 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 populations of athletes at similar schools with and without drug testing.

a) Do the data give good reason to think that drug use among athletes is lower in schools that test for drugs? State hypotheses, find the test statistic, and use either software of the bottom row of Table C (t-distribution critical values table) for the P-value. Be sure to state your conclusion.

b) You should not use the large-sample confidence interval for the difference between the proportions of athletes using drugs at schools with and without testing. Why not?