Question

Use the given information to find the number of degrees of​ freedom, the critical values chi Subscript Upper L Superscript 2 χ2L and chi Subscript Upper R Superscript 2 χ2R​, and the confidence interval estimate of sigma σ. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution.

Nicotine in menthol cigarettes 95​% confidence; n=30​, s=0.24mg.

I've figured out how to calculate the degrees of freedom and I have the formula to solve for 2 χ2L and 2 χ2R. But I'm not sure how to find it on my calculator. Or how to find 2 χ (alpha)/2

If someone could please help me with that, that'd be great. Thank you.

Answer 1

Solution :

Given that,

s = 0.24

s² = 0.0576

²_L = ²_/2,df = 45.722

²_R = ²_{1 - /2,df} = 16.047

The 95% confidence interval for is,

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

  29 * 0.0576 / 45.722 < < 29 * 0.0576 / 16.047

0.19 < < 0.32

(0.19 , 0.32 )