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, 6 of 112 athletes at Wahtonka and 24 of 102 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?

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 99.5% confidence interval for the difference between the proportion of athletes using drugs at schools with and without testing.
Interval: _______ to ________

Answer 1

a)

since success sample is less than 10 for Wahtonka

at least one of the sample has fewer success

b)

adding 1 to success and 2 in sample size in both the groups

Wahtonka sample size =114 ; Wahtonka drug users =7

Warrenton sample size =104 ; Warrenton drug users =25

c)

x=	7	25
p̂=x/n=	0.0614	0.2404
n =	114	104
estimated diff. in proportion=p̂1-p̂2=		-0.1790
Se =√(p̂1*(1-p̂1)/n1+p̂2*(1-p̂2)/n2) =		0.0476
for 99.5 % CI value of z=		2.807
margin of error E=z*std error =		0.133484
lower bound=(p̂1-p̂2)-E=		-0.3125
Upper bound=(p̂1-p̂2)+E=		-0.0455
from above 99.5% confidence interval for difference in population proportion =(-0.3125 to -0.0455)