Question

n a random sample of 23 ​people, the mean commute time to work was 32.6 minutes and the standard deviation was 7.3 minutes. Assume the population is normally distributed and use a​ t-distribution to construct a 90​% 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.

Answer 1

Solution :

The 90% confidence interval for mean is given as follows :

Where, x̅ is sample means, s is sample standard deviation, n is sample size and t_{(0.10/2, n - 1)} is critical t-value to to construct 90% confidence interval.

Note : The term after the plus minus sign is known as margin of error.

We have, x̅ = 32.6 minutes, s = 7.3 minutes, n = 23

Using t-table we get, t_{(0.10/2, 23 - 1)} = 1.717

Hence, 90% confidence interval for population mean is,

The term after the plus minus sign is calculated to be 2.614.

Hence, margin of error = 2.614

The 90% confidence interval for population mean is (29.986 minutes, 35.214 minutes).

Interpretation : We are 90% confident that the true value of mean commute time to work lies between 29.986 minutes and 35.214 minutes.