Question

In a random sample of 28 ​people, the mean commute time to work was 33.6 minutes and the standard deviation was 7.1 minutes. Assume the population is normally distributed and use a​ t-distribution to construct a 99​% confidence interval for the population mean μ. What is the margin of error of μ​? Interpret the results.

Answer 1

Solution :

t _/2,df = 2.771

Margin of error = E = t_/2,df * (s /n)

= 2.771 * (7.1 / 28)

Margin of error = E = 1.83

The 95% confidence interval estimate of the population mean is,

- E < < + E

33.6 - 1.83 < < 33.6+ 1.83

31.77 < < 35.43

(31.77 , 35.43)