Question

In a random sample of 29 ​people, the mean commute time to work was 30.1 minutes and the standard deviation was 7.2 minutes. Assume the population is normally distributed and use a​ t-distribution to construct a 80​% confidence interval for the population mean μ? What is the margin of error of μ​? Interpret the results.

Answer 1

df = n -1 = 29 - 1 = 28

t critical value at 0.20 significance level with 28 df = 1.313

Margin of error = t * S / sqrt(n)

= 1.313 * 7.2 / sqrt(29)

= 1.755

80% confidence interval for is

- E < < + E , Where E is margin of error.

30.1 - 1.755 < < 30.1 + 1.755

28.345 < < 31.855

80% CI Is ( 28.345 , 31.855 )

Interpretation -

We are 80% confident that true mean of commute time to work is between 28.345 min and 31.855 min