Perform the Required Hypothesis Test for Two Population Standard Deviations $\quad 8.0,8.1,8.0,8.1,7.9,8.0,7.9,8.0,8.1$

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.
-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 9 bottles filled by the new machine and 10 bottles filled by the old machine yielded the following volumes of juice (in fluid ounces). New machine: $\quad 8.0,8.1,8.0,8.1,7.9,8.0,7.9,8.0,8.1$ Old machine: $\quad 8.2,8.0,7.9,7.8,8.5,8.1,8.1,8.2,7.9,7.9$ Do the data provide sufficient evidence to conclude that there is less variation in the volumes of juice filled by the new machine than in the volumes of juice filled by the old machine? Perform an F-test at the $10 \%$ significance level. (Note: $\mathrm { s } _ { 1 } = 0.0782 , \mathrm {~s} _ { 2 } = 0.2066$ )