Question

The following sample of weights was taken from 8 cookies off the assembly line. Construct the 95% confidence interval for the population standard deviation for all cookies that come off the assembly line. Round your answers to two decimal places. 7.4,6.6,6.6,6.6,6.9,7.5,6.8,7.6

Answer 1

Solution :

Given that,

s = 0.4309

s² = 0.1857

n = 8

Degrees of freedom = df = n - 1 = 7

At 95% confidence level the ² value is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

1 - / 2 = 1 - 0.025 = 0.975

²_L = ²_/2,df = 16.013

²_R = ²_{1 - /2,df} = 1.690

The 95% confidence interval for is,

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

  7 * 0.1857 / 16.03 < < 7 * 0.1857 / 1.690

0.28 < < 0.88

(0.28 , 0.88)