Question

In a random sample of 26 ​people, the mean commute time to work was 33.8 minutes and the standard deviation was 7.2 minutes. Assume the population is normally distributed and use a​ t-distribution to construct a 95​% confidence interval for the population mean mu. What is the margin of error of mu​? Interpret the results. The confidence interval for the population mean mu is left parenthesis nothing comma nothing right parenthesis . (Round to one decimal place as​ needed.)

Answer 1

Solution:

Given:

Sample size = n = 26

Sample mean = minutes

Sample standard deviation = s = 7.2 minutes.

Confidence level = c = 95%

Formula:

where

t_c is t critical value for c = 95%  confidence level

Thus two tail area = 1 - c = 1 - 0.95 = 0.05

df = n - 1 =  26 - 1 = 25

Look in  t table for df = 25 and two tail area = 0.05 and find t critical value

t_c = 2.060

Thus

Thus margin of error =

Confidence interval:

Interpretation:

We are 95% confident that the true value of population mean commute time to work is between 30.9 minutes and 36.7 minutes.