The 95% confidence interval estimate of a population variance when a sample variance of 324 is obtained from a sample of 81 items is

A) 14.14 to 174.94.
B) 243.086 to 453.520.
C) 16.42 to 194.35.
D) 254.419 to 429.203.

Question

Ockacia Sterling · Accepted Answer

Final Answer : B, Explanation :   The 95% confidence interval for a population variance is calculated using the chi-square distribution with the formula:   [ ( ( n − 1 ) s 2 χ α / 2 , n − 1 2 ) , ( ( n − 1 ) s 2 χ 1 − α / 2 , n − 1 2 ) ] [(\frac{(n-1)s^2}{\chi^2_{\alpha/2,n-1}}), (\frac{(n-1)s^2}{\chi^2_{1-\alpha/2,n-1}})] [( χ α /2 , n − 1 2 ​ ( n − 1 ) s 2 ​ ) , ( χ 1 − α /2 , n − 1 2 ​ ( n − 1 ) s 2 ​ )]  , where   n n n   is the sample size,   s 2 s^2 s 2   is the sample variance, and   χ α / 2 , n − 1 2 \chi^2_{\alpha/2,n-1} χ α /2 , n − 1 2 ​   and   χ 1 − α / 2 , n − 1 2 \chi^2_{1-\alpha/2,n-1} χ 1 − α /2 , n − 1 2 ​   are the chi-square values for   α / 2 \alpha/2 α /2   and   1 − α / 2 1-\alpha/2 1 − α /2   degrees of freedom, respectively. Given   n = 81 n=81 n = 81  ,   s 2 = 324 s^2=324 s 2 = 324  , and a 95% confidence level (  α = 0.05 \alpha=0.05 α = 0.05  ), the correct interval is calculated using the appropriate chi-square values for 80 degrees of freedom, which results in option B being the correct interval.

The 95% confidence interval estimate of a population variance when a sample variance of 324 is obtained from a sample of 81 items is

A) 14.14 to 174.94.
B) 243.086 to 453.520.
C) 16.42 to 194.35.
D) 254.419 to 429.203.

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Learning Objectives

Related questions

The 95% confidence interval estimate of a population variance when a sample variance of 324 is obtained from a sample of 81 items isA) 14.14 to 174.94.B) 243.086 to 453.520.C) 16.42 to 194.35.D) 254.419 to 429.203.

Definitions

Learning Objectives

Learning Objectives

Related questions

The 95% confidence interval estimate of a population variance when a sample variance of 324 is obtained from a sample of 81 items is

A) 14.14 to 174.94.
B) 243.086 to 453.520.
C) 16.42 to 194.35.
D) 254.419 to 429.203.