Question

The following sample of lengths was taken from 8 nails off the assembly line. Construct the 90% confidence interval for the population variance for all nails that come off the assembly line. Round your answers to two decimal places.

19.3,19.1,19.6,19.7,19.1,19.2,19.0,19.0

Lower Endpoint: ??? and Upper Endpoint: ???

Answer 1

Solution :

Given that,

19.3,19.1,19.6,19.7,19.1,19.2,19.0,19.0

Point estimate = s² = 0.07

n = 8

Degrees of freedom = df = n - 1 = 8 - 1 = 7

At 90% confidence level the ² value is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

1 - / 2 = 1 - 0.05 = 0.95

²_L = ²_/2,df = 14.067

²_R = ²_{1 - /2,df} = 2.167

The 95% confidence interval for ² is,

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

7 * 0.07 / 14.067 < ² < 7 * 0.07 / 2.167

0.04 < ² < 0.23

Lower endpoint = 0.04

Upper endpoint = 0.23  

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