To perform diagnostics on the consistency of a laboratory scale, multiple measurements are taken using a reference weight over the course of several days.The variance observed over 20 repeated measures is 248.What is a 99% confidence interval for the measurement variance of this scale?
A) (122.129, 688.486)
B) (11.051, 26.239)
C) (117.809, 633.862)
D) (174.034, 413.213)

Question

Quizplus · Accepted Answer

The 99% confidence interval for the variance can be calculated using the chi-square distribution with the formula: $[ \frac{(n-1)s^2}{\chi^2_{\alpha/2, n-1}} , \frac{(n-1)s^2}{\chi^2_{1-\alpha/2, n-1}} ]$ where $n$ is the sample size, $s^2$ is the sample variance, and $\chi^2$ values are taken from the chi-square distribution table for $n-1$ degrees of freedom at the specified confidence level. Given $n=20$, $s^2=248$, and a 99% confidence level, the calculated interval falls into the range given in option A.

To Perform Diagnostics on the Consistency of a Laboratory Scale