Question

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 136 athletes at Wahtonka and 21 of 116 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?
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 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:      Wahtonka drug users:  
Warrenton sample size:      Warrenton drug users:

(c) Give the plus four 99% confidence interval for the difference between the proportion of athletes using drugs at schools with and without testing.
Interval:

Answer 1

a)

since success for Wahtonka is 5 which is less than 10 ,

At least one sample has too few successes.

b)

we add 1 in success and 2 in total sample size for each group

Wahtonka: sample size=138 drug users=6

Warranton: sample size=118 drug users=22

c)

	Boys	Girls
x=	6	22
p̂=x/n=	0.0435	0.1864
n =	138	118
estimated diff. in proportion=p̂1-p̂2=		-0.1430
Se =√(p̂1*(1-p̂1)/n1+p̂2*(1-p̂2)/n2) =		0.0398
for 99 % CI value of z=		2.576
margin of error E=z*std error =		0.1026
lower bound=(p̂1-p̂2)-E=		-0.2456
Upper bound=(p̂1-p̂2)+E=		-0.0404

from above 99% confidence interval for difference in population proportion =(-0.2456 , -0.0404)