Which of the following is a 98% confidence interval for the population variance when the sample variance is 20 for a sample of 10 items from a normal population?
A) [8.308, 86.207]
B) [7.476, 77.512]
C) [8.617, 78.125]
D) [7.755, 70.313]

Question

Quizplus · Accepted Answer

The confidence interval for the population variance $\sigma^2$ when the sample variance $s^2$ is known can be calculated using the chi-square distribution: $\left[\frac{(n-1)s^2}{\chi^2_{\alpha/2, n-1}}, \frac{(n-1)s^2}{\chi^2_{1-\alpha/2, n-1}}\right]$, 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 critical values of the chi-square distribution for $n-1$ degrees of freedom at the respective tails of the distribution. For a 98% confidence interval and a sample size of 10 (thus 9 degrees of freedom), and given that the sample variance is 20, the correct interval can be calculated using the appropriate chi-square distribution values. Choice A provides the interval that correctly corresponds to these calculations.

Which of the Following Is a 98% Confidence Interval for the Population