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=2525​, s=0.270.27mg.

Answer 1

SOLUTION:

From given data,

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 = 25​, s = 0.27 mg.

The number of degrees of freedom Is the sample size minus 1.

We are given sample size, n = 25 .

Therefore, the number of degrees of freedom is shown below

degrees of freedom(df)= n-1=25-1=24

Level of significance corresponds to 90% confidence level or C=0.90 Is shown below.

=1-C

=1-0.90

= 0.1

We divide = 0.1 equally between the two tails of the chi-square distribution

/2 or 0.10 /2 =0.05 in each tail .

We refer to the values of df =24

The critical values are ,

= =17.708 and

= = 42.557  
Sample standard deviation is s = 0 27

The 90% confidence Interval by evaluating the following:

sqrt((n-1)s² / ) <   < sqrt((n-1)s² / )

sqrt((25-1)0.27² / 42.557) <   < sqrt((25-1)0.27² / 17.708)

0.202760 <   < 0.314329

Lower bound: 0.2027

Upper bound: 0.3143