Question

Use the given information to find the number of degrees of​ freedom, the critical values 2χ2L and 2χ2R​, and the confidence interval estimate of sigmaσ. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution. Nicotine in menthol cigarettes 90% ​confidence; n=30​, s=0.23 mg.

Answer 1

Solution :

Given that,

s = 0 .23

s² = 0 .0529

n = 30

Degrees of freedom = df = n - 1 = 30 -1 =29

At 90% confidence level the ² value is ,

= 1 - 90 % =1 - 0.90=0.1

/ 2 = 0.1 / 2 = 0.05

1 - / 2 = 1 - 0.05 = 0.95

²_L = ²_/2,df = 42.557

²_R = ²_{1 - /2,df} = 17.708

The 90% confidence interval for is,

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

29 * 0.0529 / 42.557 < < 29 *0.0529 / 17.708

0.19 < < 0.29

( 0.19,0.29 )