A test concerning some of the fundamental facts about AIDS was administered to two groups, one consisting of college graduates and the other consisting of high school graduates. A summary of test results follows:

College graduates:

n $=100,$ x $=80\mathrm{.}5,$ s $=6\mathrm{.}5$

High school graduates:

n$=100,$ x $=53\mathrm{.}4,$ s $=10\mathrm{.}7$

a$.$ Test at the $0\mathrm{.}05$ level of significance whether the two sets of scores are equally

variable or whether college graduates$$ scores are less variable than high school

graduate$$ scores. What assumption$($s$)$ are necessary?

b$.$ Based on your conclusion in $($i$),$ would you pool the sample variances or not?

Explain.

c$.$ Do these data show that the college graduates, on the average, score significantly higher on the test? Test the hypothesis using alpha$=0\mathrm{.}05.$