Use the Two-Standard-Deviations F-Interval Procedure to Find the Required Confidence $\quad 8.1,8.0,8.0,8.1,8.0,7.9,8.0,7.9,8.2,8.0$

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.
-The manager of a juice bottling factory is considering installing a new juice bottling machine which she hopes will reduce the amount of variation in the volumes of juice dispensed into 8-fluid-ounce
Bottles. Random samples of 10 bottles filled by the old machine and 9 bottles filled by the new
Machine yielded the following volumes of juice (in fluid ounces) .
Old machine:
$\quad 8.1,8.0,8.0,8.1,8.0,7.9,8.0,7.9,8.2,8.0$
New machine:
$\quad 8.0,8.1,8.0,8.1,7.9,8.0,7.9,8.0,8.1$
Construct a $90 \%$ confidence interval for the ratio, $\sigma _ { 1 } / \sigma _ { 2 }$ , where $\sigma _ { 1 }$ is the population standard deviation of the volumes of juice dispensed by the old machine and $\sigma _ { 2 }$ is the population standard deviation of the volumes of juice dispensed by the new machine. (Note: $s _ { 1 } = 0.0919 , s _ { 2 } = 0.0782$ )

A) $0.92$ to $2.57$
B) $0.55$ to $2.02$
C) $0.74$ to $2.30$
D) $0.64$ to $2.11$