Question

The question is:
From a normal population, a sample of 25 elements was extracted and a standard deviation of 45 was obtained. Determine a 99% confidence interval for the population variance.

The answer is:
1157.7 ≤ σ² ≤ 5337.8

How do you get this answer?

Answer 1

The 99% confidence interval for the Population Variance is given by -

where, s is the sample standard deviation = 45

n is the sample size = 25

are the critical value of chi square with 24 degrees of freedom (as df = n - 1) at 0.005 and 0.995 probability respectively. It can be obtained from the chi square table by finding the value corresponding to 24 degrees of freedom and corresponding probabilities and are equal to 45.559 and 9.886 respectively.

It can also be calculated in Excel using the formula =CHIINV(0.005,24) and =CHIINV(1-0.005,24) respectively.

So, the confidence interval will be -