Question

A hypothetical study concerned with estimating th187e amount of marijuana use per year among a teenage population obtained a sample of ll0 high-school students. With the following sample statistics, construct a 95 confidence interval around the mean number of times this sample uses marijuana in a given 6-month period: Mean of the sample = 5.3; the standard deviation of the sample = 4.3 and the sample size = 110 What does the interval you constructed tell us about marijuana use in the population? Interpret these results.

Answer 1

sample mean, xbar = 5.3
sample standard deviation, s = 4.3
sample size, n = 110
degrees of freedom, df = n - 1 = 109

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 1.982

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (5.3 - 1.982 * 4.3/sqrt(110) , 5.3 + 1.982 * 4.3/sqrt(110))
CI = (4.49 , 6.11)

We are 95% confident that the average amount of marijuana use per year among teenage pouplation is between 4.49 and 6.11