Question

A butcher uses a machine that packages chicken livers in seven-pound portions. A sample of 72 packages of chicken livers has a variance of 0.13. Calculate a 98% confidence interval to estimate the variance of the weights of the packages prepared by the machine. Round your answers to 2 decimal places.

1 Lower Bound？

2 Upper Bound？

Answer 1

Solution :

Given that,

Point estimate = s² = 0.13

n = 72

Degrees of freedom = df = n - 1 = 71

²_L = ²_/2,df = 101.621

²_R = ²_{1 - /2,df} = 46.246

The 95% confidence interval for ² is,

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

71 * 0.13 / 101.621 < ² < 71 * 0.13 / 46.246

0.09 < ² < 0.20

Lower bound = 0.09

Upper bound = 0.20