The 95% confidence interval estimate for a population variance when a sample variance of 324 is obtained from a sample of 81 items is
A)14.14 to 174.94
B)243.087 to 453.518
C)16.42 to 194.35
D)15.591 to 21.296

Question

Quizplus · Accepted Answer

We use the chi-square distribution to calculate the confidence interval for population variance. The formula for the confidence interval is:

[(n-1)s^2/chi-square(α/2, n-1), (n-1)s^2/chi-square(1-α/2, n-1)],

where s^2 is the sample variance, n is the sample size, and α is the level of significance (1- confidence level).

Plugging in the values given in the problem, we get:

[(81-1)324/chi-square(0.025, 80), (81-1)324/chi-square(0.975, 80)]
= [243.087, 453.518]

Therefore, the 95% confidence interval estimate for the population variance is [243.087, 453.518]. The answer is B.

The 95% Confidence Interval Estimate for a Population Variance When