Question

3. The US Substance Abuse and Mental Health Services Administration conducts surveys on drug use by type of drug and age group. Results are published in National Household Survey on Drug Abuse. According to that publication, 15.0% of the 18-25 year-olds were current users of marijuana in 2000. We are interested in whether recent evidence supports that there has been a change in marijuana use since 2000.
(a) State the null and alternative hypotheses for test the claim that the proportion of marijuana users has changed since 2000.
(b) A 2014 poll of 1283 randomly selected 18-25 year-olds revealed that 205 currently use marijuana. Calculate ˆ p.
(c) Report the p-value.
(d) Did you find sufficient evidence of a change since 2000 in drug use among this age group? Give a one sentence conclusion.
(e) A confidence interval for the proportion of marijuana users in 2014 is (0.140< p <0.180)which is interpreted: We can be 95% confident that between 14% and 18% of 18-25 year-olds use marijuana. Is the confidence interval consistent with your conclusion in d)? Explain.

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.15
Alternative Hypothesis, Ha: p ≠ 0.15

b)

pcap = 205/1283 = 0.1598

c)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.1598 - 0.15)/sqrt(0.15*(1-0.15)/1283)
z = 0.98

P-value Approach
P-value = 0.3271

d)

There is not sufficient evidence of a change since 2000 in drug use among this age group

e)

yes, because confidence interval contain s15%