The values taken from a normally distributed population are 21 23 25 27 28 35 30 32 33.
Which of the following is a 95% confidence interval for the population variance?
A) [2.03, 16.30]
B) [10.12, 81.43]
C) [9.00, 72.41]
D) [11.39, 91.64]

Question

Quizplus · Accepted Answer

To calculate a 95% confidence interval for the population variance when the population is normally distributed, we use the chi-square distribution. The formula involves the sample variance $s^2$, the sample size $n$, and the chi-square values for the degrees of freedom $df = n - 1$ at the desired level of confidence. The sample variance $s^2$ is calculated based on the given data, and the chi-square values are looked up in a chi-square distribution table for $df = n - 1$ and the confidence level (95% in this case). The correct interval, [10.12, 81.43], suggests that the calculation was done correctly, taking into account the variability of the sample and using the appropriate chi-square values for the calculation.

The Values Taken from a Normally Distributed Population Are 21