A study compared the drug use of 288 randomly selected high school seniors expos
ID: 3020962 • Letter: A
Question
A study compared the drug use of 288 randomly selected high school seniors exposed to a drug education program (DARE) and 335 randomly selected high school seniors who were not exposed to such a program. Data for marijuana use are given in the accompanying table.
Is there convincing evidence that the proportion using marijuana is lower for students exposed to the DARE program? Test at the .05 significance level.
Test statistic:____ (Round answer to 2 decimals)
P-value:____ (Round answer to 4 decimals. Do NOT include leading 0's. Instead of 0.1234 enter .1234).
There ____ (is/is not) sufficient evidence to conclude that the proportion of students using marijuana is lower for students exposed to the DARE program.
Sample Size Number who use marijuana Exposed to DARE 280 135 Not exposed to DARE 330 170Explanation / Answer
Ho : p1 - p2 < 0
p1 = 135/280 = 0.4821
p2 = 170/330 = 0.5152
Z = (p1 - p2)/[(p1q1/n1) + (p2q2/n2)]
= (0.4821 - 0.5152)/[(0.4821×0.5179/280)+(0.5152×0.4848/330)]
= -0.033/(0.000892 + 0.000756)
= -0.033/0.0041
= -0.81
P-value = .2090 > 0.05
There is sufficient evidence to conclude that the proportion of students using marijuana is lower for students exposed to the DARE program.
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