Question

An apple a day: Following are the numbers of grams of sugar per 100 grams of apple in a random sample of 6 Red Delicious apples. Assume the population is normally distributed. Construct a 99% confidence interval for the standard deviation of the number of grams of sugar. Round the answers to two decimal places.

11.9 12.4 13.2 13.5 12.2 10.4

Answer 1

sample mean, xbar = 12.27
sample standard deviation, s = 1.0985
sample size, n = 6
degrees of freedom, df = n - 1 = 5

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, tc = t(α/2, df) = 4.032

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (12.27 - 4.032 * 1.0985/sqrt(6) , 12.27 + 4.032 * 1.0985/sqrt(6))
CI = (10.46 , 14.08)