Use the Two-Standard-Deviations F-Interval Procedure to Find the Required Confidence

Multiple Choice

Use the two-standard-deviations F-interval procedure to find the required confidence interval. Assume that independentsamples have been randomly selected from the two populations and that the variable under consideration is normallydistributed on both populations.
-A researcher obtained independent random samples of men from two different towns. She recorded the weights of the men. The results are summarized below: $\begin{array} { l l } \frac { \text { Town A } } { \mathrm { n } _ { 1 } = 61 } & \frac { \text { Town B } } { \mathrm { n } _ { 2 } = 31 } \\\overline { \mathrm { x } } _ { 1 } = 165.1 \mathrm { lb } & \overline { \mathrm { x } } _ { 2 } = 159.5 \mathrm { lb } \\\mathrm { s } = 29.8 \mathrm { lb } & \mathrm { s } = 25.2 \mathrm { lb }\end{array}$
Construct a $99 \%$ confidence interval for the ratio, $\sigma _ { 1 } / \sigma _ { 2 }$ , where $\sigma _ { 1 }$ is the population standard deviation of the weights of men from town $\mathrm { A }$ and $\sigma _ { 2 }$ is the population standard deviation of the weights of men from town $B$ .

A) $0.795$ to $1.685$
B) $0.489$ to $2.59$
C) $0.76$ to $1.75$
D) $0.76$ to $1.84$