Question

A random sample of 61 Foreign Language movies made in the last 10 years has a mean length of 135.7 minutes with a standard deviation of 13.7 minutes. Construct a 95% confidence interval.

Answer 1

95% confidensce interval of the mean (two-tail) = [132.2, 139.2]

Explanation:

Given:

N = size of sample = 61

m = sample mean = 135.7

s = sample standard deviation 13.7

Need 95% confidence interval

Solution.

alpha (95% confidence interval) = 0.05

(1-alpha/2) = 0.975 [two sided]

Equation for confidence interval of the mean

= m +/- t(1-alpha/2,N-1) * s / sqrt(N)

= 135.7 +/- 2.0003 * 13.7 / sqrt(60)

= [132.16, 139.24]