The mean replacement time for a random sample of 12 CD players is $8.6$ years with a standard deviation of $4.4$ years. Construct the $99 \%$ confidence interval for the population variance, $\sigma ^ { 2 }$. Assume the data are normally distributed, and round to the nearest hundredth when necessary.
A) $( 1.81,18.59 )$
B) $( 2.82,9.04 )$
C) $( 7.96,81.81 )$
D) $( 8.61,69.74 )$

Question

Quizplus · Accepted Answer

The confidence interval for the population variance is calculated using the chi-square distribution. With a sample size of 12, the degrees of freedom is 11. Using the chi-square distribution table for 99% confidence, the critical values are approximately 2.603 and 21.920. The confidence interval is calculated as $(\frac{(n-1)s^2}{\chi^2_{upper}}, \frac{(n-1)s^2}{\chi^2_{lower}})$, which results in $(7.96, 81.81)$.

The Mean Replacement Time for a Random Sample of 12 8.68.68.6

The Mean Replacement Time for a Random Sample of 12 $8.6$