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 31.9 minutes and the standard deviation was 7.2 minutes. Assume the population is normally distributed and use a t distribution to construct a 90% confidence interval for the population mean m. What is the margin error of m? Interpret results.

Solution

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

Given a=1-0.9=0.1, t(0.05, df=28) =1.70 (from student t table)

So the margin error of m is t*s/vn

= 1.7*7.2/sqrt(29)

=2.272911

So the lower bound is

xbar - t*s/vn = 31.9- 2.272911 =29.62709

So the upper bound is

xbar + t*s/vn = 31.9+ 2.272911 =34.17291

We have 90% confident that the population mean will be within this interval.