For a) and b), determine whether each statement is “true” or “false” and explain why.

a) “A statistics professor wanted to test whether the grades on a statistics test were the same for upper and lower classmen. The professor took a random sample of size 10 from each, conducted a test and found out that the variances were equal. For this situation, the professor should use a t test with related samples.”

b) “A statistics professor wanted to test whether the grades on a statistics test were the same for upper and lower classmen. The professor took a random sample of size 10 from each, conducted a test and found out that the variances were equal. For this situation, the professor should use a t test with independent samples.”

c) A Marine drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training. To test whether any improvement occurred, the instructor would use a t-distribution with how many degrees of freedom?

d) A Marine drill instructor recorded the time in which 11 recruits completed an obstacle course before basic training, and then compared those results to a sample of 11 independently selected recruits after basic training. To test whether any improvement occurred, the instructor would use a t-distribution with how many degrees of freedom?