Question

The manager of the service department of a local car dealership has noted that the service times of a sample of 15 new automobiles has a sample variance of S2 = 16. A 95% confidence interval estimate for the population variance of service times for all their new automobiles is: A. 8.576 to 39.794 B. 4.162 to 16.324 C. 4.126 to 15.760 D. 2.928 to 6.308  

Answer 1

n = sample size = 15

Sample variance = = 16

Confidence level = c = 0.95

alpha = 1 - c = 1 - 0.95 = 0.05

For a 95% confidence interval, we have alpha = 0.025 which gives 2.5% of the area at each end of the chi-square distribution.

Degrees of freedom = n - 1 = 15 - 1 = 14

95% confidence interval estimate for the population variance of service times for all their new automobiles is

From statistical table of chi square values

= 26.119 (Round to 3 decimal)   

= 5.629 (Round to 3 decimal)

(Round to 3 decimal)

95% confidence interval estimate for the population variance of service times for all their new automobiles is (8.576, 39.794)