Question

in a random sample of 17 people, the mean commute time to work was 31.2 minutes and the standard deviation was 7.1 minutes.Assume the population is normally distributed and use a t-distribution to construct a 80% confidence interval for the population mean. what is the margin of error of the mean? interpret the results. the confidence interval for the population mean is ?

Answer 1

Since , the population standard deviation is not known

Therefore , use t-distribution.

Now , df=degrees of freedom=n-1=17-1=16

The critical value is , ; From t-table

The margin of error is ,

The 80% confidence interval for the population mean is ,

Interpretation : There is 80% confident that the true population mean lies in the interval (28.8977,33.5023)