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

question 84

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 \(2.11\)

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