Question

(1 point) 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, 5 of 100 athletes at Wahtonka and 25 of 136 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) 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?

Wahtonka sample size: 102 Wahtonka drug users: 6

Warrenton sample size: 138 Warrenton drug users: 26

(c) Give the plus four 99.5% confidence interval for the difference between the proportion of athletes using drugs at schools with and without testing.

Answer 1

(a)

For a large sample confidence interval number of successes and number of failures must be greater than equal to 10.

Since sample of Wahtonka has only 6 successes so large sample confidence interval cannot be used.

(b)

Wahtonka sample size: 102

Wahtonka drug users: 6

Warrenton sample size: 138

Warrenton drug users: 26

(c)

Here we have

Let us find the standard error of estimate so

For 99.5% confidence interval z-value using excel function "=NORMSINV(0.9975)" will be 2.807 so required confidence interval is

Hence, the required confidence interval is (-0.2436, -0.0156).