Question

A commercial farm uses a machine that packages blueberries in ten pound portions. A sample of 95 packages of blueberries has a standard deviation of 0.22. Construct the 90% confidence interval to estimate the standard deviation of the weights of the packages prepared by the machine. Round your answers to two decimal places.

Answer 1

Solution :

Given that,

s = 0.22

s² = 0.0484

n = 95

Degrees of freedom = df = n - 1 = 94

At 90% confidence level the ² value is ,

²_L = ²_/2,df = 117.632

²_R = ²_{1 - /2,df} = 72.640

The 90% confidence interval for is,

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

  94 * 0.0484 / 117.632 < < 94 * 0.0484 / 72.640

0.20 < < 0.25

(0.20 , 0.25)