Use the one-standard-deviation chi-square interval procedure to obtain the specified confidence interval for the population standard deviation $\sigma$. Assume that the population has a normal distribution.
-The amounts (in ounces) of juice in eight randomly selected juice bottles are:
$ \begin{array}{llll}15.3 & 15.3 & 15.8 & 15.2 \ 15.4 & 15.3 & 15.9 & 15.2\end{array} $

Find a $98 \%$ confidence interval for the standard deviation, $\sigma$, of the amounts of juice in all such bottles.
A)$0.20$ to $0.76 \mathrm { oz }$
B) $0.16$ to $0.56 \mathrm { oz }$
C) $0.17$ to $0.64 \mathrm { oz }$
D) $0.17$ to $0.56 \mathrm { oz }$

Question

Use the one-standard-deviation chi-square interval procedure to obtain the specified confidence interval for the population standard deviation $\sigma$. Assume that the population has a normal distribution.
-The amounts (in ounces) of juice in eight randomly selected juice bottles are:
$ \begin{array}{llll}15.3 & 15.3 & 15.8 & 15.2 \ 15.4 & 15.3 & 15.9 & 15.2\end{array} $

Find a $98 \%$ confidence interval for the standard deviation, $\sigma$, of the amounts of juice in all such bottles.  
A)$0.20$ to $0.76 \mathrm { oz }$
B) $0.16$ to $0.56 \mathrm { oz }$
C) $0.17$ to $0.64 \mathrm { oz }$
D) $0.17$ to $0.56 \mathrm { oz }$

Quizplus · Accepted Answer

To find the 98% confidence interval for the standard deviation, we use the chi-square distribution with $n-1=7$ degrees of freedom. The sample variance is calculated, and the chi-square critical values for 98% confidence are used to find the interval. The correct interval is $0.17$ to $0.64 \mathrm { oz }$.

Use the One-Standard-Deviation Chi-Square Interval Procedure to Obtain the Specified σ\sigmaσ

Use the One-Standard-Deviation Chi-Square Interval Procedure to Obtain the Specified $\sigma$