In a random sample of 29 people the mean commute time to wor

In a random sample of 29 people, the mean commute time to work was 32.4 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 Mu. What is the margin of error of Mu? Interpret the results. The confidence interval for the population mean Mu is .(Round to one decimal place as needed.)

Solution

The degree of freedom =n-1=29-1=28

Given a=1-0.99=0.01, t(0.005, df=28) =2.76 (from student t table)

So the lower bound is

xbar - t*s/vn =32.4-2.76*7.1/sqrt(29) =28.8

So the upper bound is

xbar + t*s/vn =32.4+2.76*7.1/sqrt(29)= 36.0