Question

A sample of 100 obese adults from a population following a normal distribution was put on a low carbohydrate diet. For this sample, the average weight loss was 10 lb and the standard deviation was 4 lb. Find a 90% confidence interval for the variance of the population.

Answer 1

Solution :

n = 100

df = n - 1 = 99

x̄ = average weight loss = 10 lb

s = standard deviation = 4 lb

CI =confidence interval = 90%

Using Chi square Distribution, excel commands

Lower critical value = CHIINV(0.05,99) = 77.046

Upper Critical Value = CHIINV(0.95,99) = 123.225

Upper Limit = ((n-1)*s*s)/Lower critical value = (99*4*4)/77.046 = 20.5591

Lower Limit = ((n-1)*s*s)/Upper critical value = (99*4*4)/123.225 = 12.8545

The 90% confidence interval for population variance,

(12.8545 , 20.5591)