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, 4 of 125 athletes at Wahtonka and 26 of 149 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 95% confidence interval for the difference between the proportion of athletes using drugs at schools with and without testing.
Interval: ___________ to ____________

Answer 1

a)

. At least one sample has too few failures. At least one sample has too few successes

b)

adding one in success and 2 in sample size:

Wahtonka sample size: 5     Wahtonka drug users:127
Warrenton sample size: 27     Warrenton drug users: 151

c)

estimated diff. in proportion=p̂1-p̂2=		-0.1394
Se =√(p̂1*(1-p̂1)/n1+p̂2*(1-p̂2)/n2) =		0.0356

for 95 % CI value of z=		1.960	from excel:normsinv((1+0.95)/2)
margin of error E=z*std error =		0.069853
lower bound=(p̂1-p̂2)-E=		-0.2093
Upper bound=(p̂1-p̂2)+E=		-0.0696
from above 95% confidence interval for difference in population proportion =(-0.2093 ,-0.0696)