Question: Perform the following hypothesis test on the paired data below:

H_O: ?_d = 0 (Please recall that ?_d is read ~ and also known as ~ Mu-sub-d)

H_A: ?_d ≠ 0 Test at ? = 0.05

a) Is this an upper tail, lower tail, or two-tail test? (4 points)

b) Are we testing means or proportions? (4 points)

c) State the rule of rejection (in terms of p-value and level of significance) (4 points)

d) Find the p-value (4 points)

e) Should you reject or not reject H_O? (4 points)

f) Do the data provide sufficient evidence to suggest the After scores are indeed higher?

Why or why not? (4 points)

Note: Because the above is a two-tail test, rejection of Ho alone is not a sufficient reason. Hint: What else did you observe among the sample results?