Question

The manager of the service department of a local car dealership has noted that the service times of a sample of 24 new automobiles has a standard deviation of 5 minutes. A.) Compute a 90% confidence interval estimate for the standard deviation of the service times (in minutes) for all their new automobiles. B.) The manager of the service department of a local car dealership wants to test the claim that the variance of the service time does not exceed 27 minutes. Test this claim using a significance level of 0.1.

Answer 1

Part a)

(0.1/2, 24 - 1 ) = 35.1725
(1 - 0.1/2, 24 - 1) ) = 13.0905
Lower Limit = 4.0433
Upper Limit = 6.6276
90% Confidence interval is ( 4.0433 , 6.6276 )
( 4.0433 < σ < 6.6276 )

Part b)

To Test :-

H0 :- σ² > 27

H1 :- σ² ≤ 27

Test Statistic :-

= ( ( 24-1 ) * 25 ) / 27
= 21.2963

Test Criteria :-
Reject null hypothesis if
(1 - 0.1,24 - 1) = 14.848
= 21.2963 > 14.848 , hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

There is insufficient evidence to support the claim that the variance of the service time does not exceed 27 minutes.