In 2002 the Supreme Court ruled that schools could require random drug tests of students participating in competitive af

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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, 8 of 141
athletes at Wahtonka and 20 of 128 athletes at Warrenton said they
were using drugs. Regard these athletes as SRSs (simple random
samples) 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?
Choose a reason. The sample sizes are too
small. The sample sizes are not identical. The sample
proportions are too small. At least one sample has too few
failures. At least one sample has too few successes.
(b) The plus four method for a two-sample confidence interval
adds four observations in total: 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: Wahtonka
drug users:
Warrenton sample size: Warrenton drug
users:
(c) Give the plus four 96% confidence interval for the
difference between the proportion of athletes using drugs at
schools with and without testing.
Interval: _____ to ______