The manager of the service department of a local car dealership has noted that the service times of a sample of 16 new automobiles has a standard deviation of 5 minutes. A 95% confidence interval estimate for the variance of service times for all their new automobiles is
A) 13.642 to 59.885.
B) 9.46 to 34.09.
C) 2.144 to 9.948.
D) 2.728 to 11.977.

Question

Quizplus · Accepted Answer

The correct confidence interval for the variance is calculated using the chi-square distribution with the formula $\frac{(n-1)s^2}{\chi^2_{\alpha/2,n-1}}$ to $\frac{(n-1)s^2}{\chi^2_{1-\alpha/2,n-1}}$, where $n$ is the sample size, $s^2$ is the sample variance, and $\chi^2$ values are taken from the chi-square distribution table for the given confidence level (95% in this case) and degrees of freedom ($n-1$). Given $n=16$ and $s=5$, the correct interval must account for the variance ($s^2=25$) and use the appropriate chi-square values for 15 degrees of freedom, leading to the interval in option A.

The Manager of the Service Department of a Local Car