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 standard deviation of 4 minutes. A 95% confidence interval estimate for the variance of service times for all its new automobiles is _____.
A) 8.58 to 39.79
B) 4 to 16
C) 4 to 15
D) 1.64 to 1.96

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 based on the degrees of freedom ($n-1$) and the confidence level ($1-\alpha$). Given $n=15$ and $s=4$, and aiming for a 95% confidence interval, the calculation leads to the interval provided in option A, which correctly accounts for the variability in the sample to estimate the population variance.

The Manager of the Service Department of a Local Car