Question # 3

Perform the following hypothesis test on the paired data below:

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

Before 30 75 92 69 61 57 57 89 92

After 53 68 98 62 67 71 68 96 98

a) Is this an upper tail, lower tail, or two-tail test? (5 points)

b) Are we testing means or proportions? (5 points)

c) State the rule of rejection (in terms of p-value and level of significance) (5 points)

d) Find the p-value (5 points)

e) Should you reject or not reject HO? (5 points)

f) Do the data provide sufficient evidence to suggest the After scores are indeed higher? Why or why not? (5 points)

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