Answer :
Final answer:
To construct a 99% confidence interval for the variance, we can make use of the Chi-Square distribution.
Explanation:
To construct a 99% confidence interval for the variance, we can make use of the Chi-Square distribution. The formula for the confidence interval is:
(lower bound, upper bound) = [(n - 1)s^2 / χ^2(α/2, n - 1), (n - 1)s^2 / χ^2(1 - α/2, n - 1)]
Where n is the sample size, s^2 is the sample variance, α is the level of significance (1 - confidence level), and χ^2 represents the Chi-Square distribution.
Using the given data, we have n = 20 and the sample variance is calculated as:
s^2 = Σ(x - mean)^2 / (n - 1)
After calculating the sample variance, we can substitute the values into the formula to obtain the confidence interval for the variance.
The correct answer choice is A. (21.61, 69.06).
