Provide an appropriate response.
-The mean replacement time for a random sample of $12 \mathrm {~cd}$ players is $8.6$ years with a standard deviation of $5.1$ years. Construct the $98 \%$ confidence interval for the population variance, $\sigma ^ { 2 }$. Assume the data are normally distributed
A) $( 11.6,93.7 )$
B) $( 3.4,9.7 )$
C) $( 2.3,18.4 )$
D) $( 10.9,80.1 )$

Question

Quizplus · Accepted Answer

To construct a 98% confidence interval for the population variance when the sample size is 12 and the sample standard deviation is 5.1 years, we use the chi-square distribution. The formula for the confidence interval for the variance is given by $\left( \frac{(n-1)s^2}{\chi^2_{\alpha/2, n-1}}, \frac{(n-1)s^2}{\chi^2_{1-\alpha/2, n-1}} \right)$, where $n$ is the sample size, $s^2$ is the sample variance, and $\chi^2_{\alpha/2, n-1}$ and $\chi^2_{1-\alpha/2, n-1}$ are the chi-square values for $n-1$ degrees of freedom at the specified confidence level. Given $n = 12$, $s = 5.1$, and a 98% confidence level, the correct interval is $(11.6, 93.7)$, which accounts for the variability in the sample variance to estimate the population variance.

Provide an Appropriate Response 12 cd12 \mathrm {~cd}12 cd Players Is 8.68.68.6 Years with a Standard Deviation Of

Provide an Appropriate Response $12 \mathrm {~cd}$ Players Is $8.6$ Years with a Standard Deviation Of