Perform the following hypothesis test on the paired data below:

HO: µd = 0 (Please recall that µd is read ~ and also known as ~ Mu-sub-d) HA: µd ≠ 0 Test at α = 0.05

Before 30 72 97 59 61 57 57 89 92

After 57 68 98 62 67 71 68 96 98

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

b) Are we testing means or proportions?

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

d) Find the p-value
e) Should you reject or not reject HO?

f) Do the data provide sufficient evidence to suggest the After scores are indeed higher? Why or why not?

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?