An issue with legalization of medical marijuana is \"diversion\", the process in

Question

An issue with legalization of medical marijuana is "diversion", the process in which medical marijuana prescribed for one person is given, traded, or sold to someone who is not registered for medical marijuana use. The mean number of days that 119 adolescents in substance abuse treatment used medical marijuana in the last six months was 104.26. Assume the population standard deviation is 27 days. Complete parts (a) through (d) below.

a. Find a 95% confidence interval for the mean number of days, mu, of diverted medical marijuana use in the last 6 months of all adolescents in substance abuse treatment. The 95% confidence interval for mu is from ____days to ____days.

b. Find a 90% confidence interval for the mean number of days, mu, of diverted medical marijuana use in the last 6 months of all adolescents in substance abuse treatment. The 90% confidence interval for mu is from ___days to ___ days.

Explanation / Answer

mean is 104.26 and s is 27

for sample size of 119, the standard error SE is s/sqrt(N)=27/sqrt(119)=2.4751

a) z for 95% confidence is 1.96

thus lower bound is mean-z*SE=104.26-1.96*2.4751=99.408804

upper bound is mean+z*SE=104.26+1.96*2.4751=109.111196

b) z for 90% confidence is 1.65

thus lower bound is mean-z*SE=104.26-1.65*2.4751=100.176085

upper bound is mean+z*SE=104.26+1.65*2.4751=108.343915

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