Question

The National Center for Drug Abuse is conducting a study to determine if the heroin usage among teenagers has changed. Historically, about 1.3 percent of teenagers have used heroin one or more times. In a recent study of 1800 teenagers, 35 said they had used heroin one or more times. Is there significant evidence that heroin usage among teenagers has changed? What concerns do you have about this data?

Answer 1

H0: Null Hypothesis: P = 0.013

HA: Alternative Hypothesis: P 0 013

P = Population proportion = 0.013

Q = 1 - P = 0.987

n = Sample Size = 1800

p = Sample Proportion = 35/1800 =0.0194

SE =

=

Test Statistic is given by:
Z = (0.0194 - 0.013)/0.0027 = 2.37

Take = 0.05

From Table, critical values of Z = 1.96

Since the calculated value of Z = 2.37 is greater than critical value of Z = 1.96, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that the heroin usage among teenagers has changed.

Since the conclusion based on the data is that the the heroin usage among teenagers has changed and the data shows an increase from 0.013 to 0.0194, our concern is that the heroin usage among teenagers has increased, which is not a desired development.