Construct a 95% confidence interval for the population standard deviation σof a random sample of 15 crateswhich have a mean weight of 165.2 pounds and a standard deviation of 14.5 pounds. Assume the population isnormally distributed.
A) (10.6, 22.9)
B) (112.7, 522.9)
C) (2.8, 6.0)
D) (11.1, 21.2)

Question

Quizplus · Accepted Answer

To construct a 95% confidence interval for the population standard deviation, we use the chi-square distribution because the population is assumed to be normally distributed. The formula involves the sample standard deviation (s), the sample size (n), and the chi-square values for the degrees of freedom (n-1) at the desired level of confidence. The degrees of freedom here are 15 - 1 = 14. Using the chi-square distribution table or calculator for 95% confidence and 14 degrees of freedom, we find the chi-square values and plug them into the formula for the confidence interval of the population standard deviation. The calculation results in the interval (10.6, 22.9), which matches option A.

Construct a 95% Confidence Interval for the Population Standard Deviation