The variance of the amount of drink contained in a random sa

The variance of the amount of drink contained in a random sample of 16 bottles of a certain sports drink was 2.5 ounces. Find a 95% confidence interval for this variance for all bottles of this sports drink, assuming that the amount of drink contained in the bottles is normally distributed.

Solution

for alpha = 1 - 0.95 = 0.05

alpha / 2 = 0.025

X^2 0.025,15 = 27.488

X^2 0.975,15 = 6.262

confidence interval

(15) * 2.5   / 6.262 < var   < (15) * 2.5 / 27.488

5.9885 < var < 1.36