Question

The weights of 89 randomly selected truck engines were found to have a standard deviation of 1.59 lbs. Calculate the 95% confidence interval for the population standard deviation of the weights of all new truck engines in this particular factory.

Answer 1

Solution :

Given that,

s = 1.59

s2 = 1.2610

n = 89

Degrees of freedom = df = n - 1 = 89 - 1 = 88

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

2L = 2/2,df = 115.842

2R = 21 - /2,df = 63.941

The 95% confidence interval for is,

(n - 1)s2 / 2/2 < < (n - 1)s2 / 21 - /2

(88)(1.2610) / 115.842 < < (88)(1.2610) / 63.941

0.98 < < 1.32

(0.98 , 1.32)