Perform the Required Hypothesis Test for Two Population Standard Deviations $\begin{array} { l l } \text { Men: } & 72,60,52,87,66,74,95,50,81,70,72 \\ \text { Women: } & 70,78,62,96,75,68,41,74,80,47,73,94,65 \end{array}$

Essay

Perform the required hypothesis test for two population standard deviations. Assume that independent samples havebeen randomly selected from the two populations and that the variable under consideration is normally distributed onboth populations. Use the critical-value approach.
-A researcher is interested in comparing the amount of variation in women's scores on a certain test with the amount of variation in men's scores on the same test. Random samples of 11 men and 13 women yielded the following scores: $\begin{array} { l l } \text { Men: } & 72,60,52,87,66,74,95,50,81,70,72 \\ \text { Women: } & 70,78,62,96,75,68,41,74,80,47,73,94,65 \end{array}$ Do the data provide sufficient evidence to conclude that there is less variation in men's scores than in women's scores? Perform an F-test at the 5% significance level. (Note: $\left. \mathrm { s } _ { 1 } = 13.754 \text { and } \mathrm { s } _ { 2 } = 15.588 \right)$