A NAPA Auto Parts supplier wants information about how long

A NAPA Auto Parts supplier wants information about how long car owners plan to keep their cars. A random sample of 41 car owners results in a mean of 7 years with a standard deviation of 3.75 years. Find a 95% confidence interval for the true population mean. Identify the point estimate for mean and margin of error.

Solution

point estimate for mean = 7

Given a=0.05, Z(0.025) = 1.96 (from standard normal table)

margin of error =Z*s/vn

=1.96*3.75/sqrt(41)

=1.147877

So 95% confidence interval is

xbar +/- Z*s/vn

--> 7 +/- 1.147877

--> (5.852123, 8.147877)

ME = 1.96 = 1.1479