The manager of the service department of a local car dealership has noted that the service times of a sample of 30 new automobiles has a standard deviation of 5 minutes. A 95% confidence interval estimate for the standard deviation of the service times (in minutes) for all their new automobiles is
A) 16.047 to 45.722.
B) 15.857 to 45.180.
C) 3.982 to 6.722.
D) 22.833 to 65.059.

Question

Quizplus · Accepted Answer

We would use the chi-square distribution to construct a confidence interval for the standard deviation. For a 95% confidence interval with 29 degrees of freedom (30-1), the chi-square values are 15.07 (from chi-square table or calculator) and 46.98 (from chi-square table or calculator).

Thus, the confidence interval estimate for the standard deviation of service times is:

sqrt[(29)(5^2)/46.98] to sqrt[(29)(5^2)/15.07]

Simplifying, we get:

3.982 to 6.722

Therefore, the answer is C.

The Manager of the Service Department of a Local Car