Question

You have been hired to do research on the prevalence of marijuana use among U.S. teenagers. You have decided to use the 2018 Monitoring the Future data that has a scale (from 0-14) measuring the number of days in the past two weeks that teens used marijuana. According to the data, this sample of 945 teens’ average marijuana use was 1.22 days per two weeks, with a standard deviation of .76. (worth 16 points total)

A. Construct the 99% confidence interval for marijuana use in the study population. Show your work.

B. Interpret the 99% confidence interval.

C. Construct the 90% confidence interval for marijuana use in the study population. Show your work.

D. Interpret the 90% confidence interval.

E. The Centers for Disease Control (CDC) has stated it will provide states with funds for marijuana prevention programs for teens if their occurrence of use exceeds 50% of a given week. Would the CDC funding kick in based on the data you calculated in parts a-d above? Justify your answer.

Answer 1

SOLUTION A] sample Mean = 1.22
t critical = 2.58
sM = √(0.762/945) = 0.02
μ = M ± t(sM)
μ = 1.22 ± 2.58*0.02
μ = 1.22 ± 0.0516

99% CI [1.1684, 1.2716].

SOLUTION B] You can be 99% confident that the population mean (μ) for average marijuana used  falls between 1.1684 and 1.2716

SOLUTION C] M = 1.22
tCRITICAL= 1.65
sM = √(0.762/945) = 0.02
μ = M ± t(sM)
μ = 1.22 ± 1.65*0.02
μ = 1.22 ± 0.033

90% CI [1.187, 1.253].

SOLTION D] You can be 90% confident that the population mean (μ) falls between 1.187 and 1.253

SOLUTION E] YES the CDC funding kick in based on the data . Because the sample is large enough to agreed with the statement.