The dean of students of a large community college claims tha

The dean of students of a large community college claims that the average distance that commuting students travel to the campus is 32 miles. The commuting students feel otherwise. A sample of 64 students was randomly selected and yielded a mean of 35 miles and a standard deviation of 5 miles. Find and interpret the 90% confidence interval for the average distance that commuting students travel to the campus. Show work please!!! Thank you!

Solution

Given a=1-0.90 =0.1, Z(0.05) = 1.645 (from standard normal table)

So the lower bound is

xbar - Z*s/vn =35 -1.645*5/sqrt(64) =33.97187

So the upper bound is

xbar + Z*s/vn =35 +1.645*5/sqrt(64) =36.02813