A random sample of 15 crates have a mean weight of 165.2 pounds and a standard deviation of 15.3 pounds. Construct a 95% confidence interval for the population standard deviation ?. Assume the population is normally distributed, and round to the nearest hundredth when necessary.
A) (2.86, 6.17)
B) (125.47, 582.24)
C) (11.76, 22.33)
D) (11.2, 24.13)

Question

Quizplus · Accepted Answer

The correct answer is D.The formula for the confidence interval for the population standard deviation is:(n-1)s^2 / chi-squared(n-1, alpha/2), (n-1)s^2 / chi-squared(n-1, 1-alpha/2)where n is the sample size, s is the sample standard deviation, and alpha is the significance level.Plugging in the values from the question, we get:(15-1)15.3^2 / chi-squared(14, 0.025), (15-1)15.3^2 / chi-squared(14, 0.975)= 11.2, 24.13Therefore, the 95% confidence interval for the population standard deviation is (11.2, 24.13).

A Random Sample of 15 Crates Have a Mean Weight