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 is interested in comparing the amount of variation in women's scores on a certain test and the amount of variation in men's scores on the same test. Independent random samples of 11 Men and 13 women yielded the following scores. $\begin{array} { l l } \text { Men: } & 72,60,52,87,66,74,95,50,81,70,72 \ \text { Women: } & 70,78,62,96,75,68,41,74,80,47,73,94,65 \end{array}$
Construct a $95 \%$ confidence interval for the ratio, $\sigma _ { 1 } / \sigma _ { 2 }$, where $\sigma _ { 1 }$ is the population standard deviation of the scores for men and $\sigma _ { 2 }$ is the population standard deviation of the scores for women.
(Note: $s _ { 1 } = 13.754$ and $s _ { 2 } = 15.588$ )
A)$0.62$ to $2.16$
B) $0.26$ to $3.20$
C) $0.48$ to $1.68$
D) $0.48$ to $1.62$

Question

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 is interested in comparing the amount of variation in women's scores on a certain test and the amount of variation in men's scores on the same test. Independent random samples of 11 Men and 13 women yielded the following scores. $\begin{array} { l l } \text { Men: } & 72,60,52,87,66,74,95,50,81,70,72 \ \text { Women: } & 70,78,62,96,75,68,41,74,80,47,73,94,65 \end{array}$
Construct a $95 \%$ confidence interval for the ratio, $\sigma _ { 1 } / \sigma _ { 2 }$, where $\sigma _ { 1 }$ is the population standard deviation of the scores for men and $\sigma _ { 2 }$ is the population standard deviation of the scores for women.
(Note: $s _ { 1 } = 13.754$ and $s _ { 2 } = 15.588$ )  
A)$0.62$ to $2.16$
B) $0.26$ to $3.20$
C) $0.48$ to $1.68$
D) $0.48$ to $1.62$

Quizplus · Accepted Answer

The confidence interval for the ratio of standard deviations is calculated using the F-distribution. Given the sample standard deviations $s_1 = 13.754$ and $s_2 = 15.588$, and the sample sizes, the interval $0.48$ to $1.68$ is the correct range for the ratio $\sigma_1 / \sigma_2$.