In 2002 the Supreme Court ruled that schools could require random drug tests of

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, 7 of 135 athletes at Wahtonka and 27 of 141 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. Do the data give good reason to think that drug use among athletes is lower in schools that test for drugs? Let Group 1 be the schools that test for drugs Let Group 2 be the schools that do not test for drugs (a) The hypotheses to be tested are O Ho. P1 2 P2 versus Ha: P P2 O Ho: P1 2 P2 versus Ha P1 P2 O Ho: X12 X2 versus Ha X1

Explanation / Answer

(a) Option (1) is the answer

(b)

Data:

n1 = 135

n2 = 141

p1 = 0.051851852

p2 = 0.191489362

Hypotheses:

Ho: p1 p2

Ha: p1 < p2

Decision Rule:

= 0.05

Lower Critical z- score = -1.644853627

Reject Ho if z < -1.644853627

Test Statistic:

Average proportion, p = (n1p1 + n2p2)/(n1 + n2) = (135 * 0.0518518518518519 + 141 * 0.191489361702128)/(135 + 141) = 0.123188406

q = 1 - p = 1 - 0.123188405797101 = 0.876811594

SE = [pq * {(1/n1) + (1/n2)}] = (0.123188405797101 * 0.876811594202899 * ((1/135) + (1/141))) = 0.039574566

z = (p1 - p2)/SE = (0.0518518518518519 - 0.191489361702128)/0.0395745659174479 = -3.53

p- value = 0.0002

(c) Option (1) is the answer

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