Do humans have free will or are we hamstrung by greater forces (or even ourselves!)? Let's find out. Say aloud the colors you see for the below text (see PDF for colored text):

List 1: house goodbye paper cow clown eat ...

List 2: yellow green orange white purple black ...

If you're like most people, List 2 was harder. This is known as the Stroop effect, and it sug- gests that your own mind might block you from your goals in life.

You decide to test if the Stroop effect is present in non-colorblind college students, so you recruit a dozen random students at various colleges and have each person read both List 1 and 2 (you randomize who gets which one first) recording how many answers were correct. You get the below sumamrized results:

List 1 - List 2

Mean: List 1: 96.3, List 2: 84.1, List 1 - List 2: 12.2
SD: List 1: 1.4, List 2: 7.3, List 1 - List 2: ?
n: List 1: 12, List 2: 12, List 1 - List 2: 12

a. Explain why the ? cannot be found using the Var(X-Y) formula

b. You wish to conduct a HT exploring if the average score on List 1 is higher than that of List 2. What value should ? be if you want a P-value of 0.02?