A sample standard deviation and sample size are given. Use the one-standard-deviation $\chi ^ { 2 }$ -interval procedure to obtainthe specified confidence interval.
-s = 6, n = 18 , 99% confidence interval
A)4.139 to 10.365
B)4.28 to 9.773
C)0.693 to 4.342
D)1.69 to 4.231

Question

A sample standard deviation and sample size are given. Use the one-standard-deviation $\chi ^ { 2 }$ -interval procedure to obtainthe specified confidence interval.
-s = 6, n = 18 , 99% confidence interval 
A)4.139 to 10.365
B)4.28 to 9.773
C)0.693 to 4.342
D)1.69 to 4.231

Quizplus · Accepted Answer

The correct confidence interval is calculated using the chi-square distribution for the variance and then taking the square root to get the standard deviation interval. The formula for the interval is $\sqrt{\frac{(n-1)s^2}{\chi^2_{\alpha/2}}}$ to $\sqrt{\frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}}$, where $n$ is the sample size, $s$ is the sample standard deviation, and $\chi^2_{\alpha/2}$ and $\chi^2_{1-\alpha/2}$ are the chi-square values for $\alpha/2$ and $1-\alpha/2$ degrees of freedom, respectively. For a 99% confidence interval and 17 degrees of freedom (n-1 for n=18), the chi-square values can be looked up in a chi-square distribution table or calculated using statistical software. The calculation results in the interval 4.139 to 10.365, which matches option A.

A Sample Standard Deviation and Sample Size Are Given χ2\chi ^ { 2 }χ2

A Sample Standard Deviation and Sample Size Are Given $\chi ^ { 2 }$