A clinical psychologist wished to compare three methods for reducing hostility levels in university students, and used a certain test $($HLT$)$ to measure the degree of hostility. A high score on the test indicated great hostility. The psychologist used $21$ students who obtained high and nearly equal scores in the experiment. Seven were selected at random from among the $21$ problem cases and were treated with method $1.$ Six of the remaining $14$ students were selected at random and treated with method $2.$ The remaining eight students were treated with method $3.$ All treatments were continued for a one$-$semester period. Each student was given the HLT test at the end of the semester, with the results shown in the table below.

$\backslash$table$[[$Method$,$Sample$],[1,90,75,91,85,83,91,82,,,],[2,77,76,72,73,78,71,,,,],[3,65,73,69,66,77,73,70,74,,]]$

$($a$)$ Use these data to perform an analysis of variance to determine whether there are differences among mean scores for the three methods. Use $=0\mathrm{.}05.$

$($b$)$ Run a F$-$test to test the equality of the population variances with $=0\mathrm{.}05.$

$($c$)$ Apply the Power Transform to the given data.

$($d$)$ Repeat $($b$)$ after the Power transformation.