Question

You want to estimate the average number of times teenagers between the ages of 13 and 18 who have smoked cannabis. You take a random sample of 25 students in Raleigh and find that on average the sample smoked marijuana 128 days in the last 12 months with an SS of 180. Calculate a 95% confidence interval around the North Carolina sample. Make sure to show all four steps

Answer 1

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 128

SS = 180

n = 25

n - 1 = 24

Variance = SS/(n - 1) = 180/24 = 7.5

S = sqrt(7.5) = 2.738613

df = n – 1 = 24

Confidence level = 95%

Critical t value = 2.0639

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 128± 2.0639*2.738613/sqrt(25)

Confidence interval = 128 ± 1.1304

Lower limit = 128 - 1.1304 = 126.87

Upper limit = 128 + 1.1304 =129.13

Confidence interval = (126.87, 129.13)