Question

Use the given information to find the number of degrees of freedom, the critical values 2χ2L and 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 98​% ​confidence; n= 27​, s=0.27 mg.

df=

2χ2L=___

​(Round to three decimal places as​ needed.)

2χ2=____

​(Round to three decimal places as​ needed.)

The confidence interval estimate of σ is ___mg < σ <___mg.

​(Round to two decimal places as​ needed.)

Answer 1

Solution :

Given that,

s = 0.27

s² = 0.0729

n = 27

Degrees of freedom = df = n - 1 = 26

At 98% confidence level the ² value is ,

²_L = ²_/2,df = 45.642

²_R = ²_{1 - /2,df} = 12.198

The 98% confidence interval for is,

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

  26 * 0.0729 / 45.642 < < 26 * 0.0729 / 12.198

0.20 < < 0.39

0.20 mg < < 0.39 mg