Question

One type of cookie manufactured by Haddad Food Company is Cocoa Cookies. A machine fills packages of these cookies. From time to time the quality control inspector at the company selects a sample of a few such packages, calculates the variance of the net weights of these packages, and constructs a 95% confidence interval for the population variance and standard deviation. A recently taken random sample of 25 packages from the production line gave a sample standard deviation of .15. Find the 95% confidence interval for standard deviation and variance.

Answer 1

Solution :

Given that,

s = 0.15

Point estimate = s² = 0.0225

df = 24

²_R = ²_/2,df = 39.364

²_L = ²_{1 - /2,df} = 12.401

(a)

The 95% confidence interval for ² is,

(n - 1)s² / ²_/2 < ² < (n - 1)s² / ²_{1 - /2}

24 * 0.0225 / 39.364 < ² < 24 * 0.0225 / 12.401

0.0137 < ² < 0.0435

(0.0137 , 0.0435)

b)

The 95% confidence interval for is,

0.1171 < < 0.2087

(0.1171 , 0.2087)