# Testing hypotheses about the population mean

Fast Service, a chain of automotive tune-up shops, advertises that its personnel can change the oil, replace the oil filter, and lubricate any standard automobile in 15 minutes, on the average. The National Business Bureau received complaints from customers that service takes considerably longer. To check the fast service claim, the Bureau had service done on 21 unmarked cars. The mean service time was 18 minutes and the standard deviation of the sample was 1 minute. Use the .05 significance level to check the reasonableness of the fast service claim.

Â© BrainMass Inc. brainmass.com March 4, 2021, 5:43 pm ad1c9bdddfhttps://brainmass.com/statistics/hypothesis-testing/testing-hypotheses-population-mean-8021

#### Solution Preview

Solution. Let X be the service time. We can assume that X follows normal distribution, X~N(a, b^2), where a is the mean of X and b is the standard deviation of X. Define Null hypothesis:

Ho: a=15 (minutes)

H1: a is not equal 15.

By the ...

#### Solution Summary

The solution contains detailed explanation of testing whether the population mean is different from a given value.