Question

A sample of N = 30 individuals is taken and it is found that the mean commute time to work for these individuals is 35 minutes with a sample standard deviation of 10 minutes. Find a 99% confidence interval for the mean commute time to work.

Answer 1

Sample mean (xbar) = 35 min

Sample standard deviation (s) = 10 min

n = 30

Here sample size is not large enough and population standard deviation is unknown so, we are using t distribution.

99% confidence interval is given by

xbar ±t_29,0.005*s/√n = 35 ± 2.756*10/sqrt(30) = (29.9683, 40.0317).

The 99 % confidence for the mean commute time to work is 29.97 min< μ < 40.03 min.