Find the 95% confidence interval for the variance of the lengths of pipes if a sample of 16 pipes has a standard deviation of 12 inches.
A) $14.0

Question

Find the 95% confidence interval for the variance of the lengths of pipes if a sample of 16 pipes has a standard deviation of 12 inches. 
A) $14.0 < \sigma ^ { 2 } < 10.0$
B) $8.9 < \sigma ^ { 2 } < 18.6$
C) $128.0 \sigma ^ { 2 } < 160.0$
D) $78.6 < \sigma ^ { 2 } < 344.9$

Quizplus · Accepted Answer

The 95% confidence interval for the variance is calculated using the chi-square distribution with n-1 degrees of freedom. For a sample size of 16, the interval is calculated as $(n-1)s^2/\chi^2_{upper}$ to $(n-1)s^2/\chi^2_{lower}$, which results in the interval $78.6 < \sigma^2 < 344.9$.

Find the 95% Confidence Interval for the Variance of the Lengths