Psychologists wish to evaluate the consistency of a standardized behavioral test.The test is designed to have a variance of 225.Twenty randomly sampled tests yield a variance of 240.Assuming the underlying population is normal, what is a 90% confidence interval for the variance of this test?
A) (151.276, 450.727)
B) (12.300, 21.230)
C) (190.542, 328.899)
D) (138.803, 511.986)

Question

Quizplus · Accepted Answer

The confidence interval for the variance of a normally distributed population, based on a sample variance, can be calculated using the chi-square distribution. The formula for the confidence interval is given by $\left[\frac{(n-1)s^2}{\chi^2_{\alpha/2}}, \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}\right]$, where $n$ is the sample size, $s^2$ is the sample variance, and $\chi^2_{\alpha/2}$ and $\chi^2_{1-\alpha/2}$ are the critical values of the chi-square distribution for $n-1$ degrees of freedom at the specified confidence level. Given $n=20$, $s^2=240$, and a 90% confidence level, the correct interval is (151.276, 450.727).

Psychologists Wish to Evaluate the Consistency of a Standardized Behavioral