FILEFor scholarship purposes, tw o graduate faculty members rate 12 applicants to the PhD program on a scale of 1 to 10 (with 10 indicating an excellent candidate).

These ratings are shown in the follow ing table and are also available on the text website, labeled PhD Rating.

Candidate Faculty A's Rating Faculty B's Rating Candidate Faculty A's Rating Faculty B's Rating 1 5 6 7 2 2 2 7 8 8 8 9 3 8 5 9 9 10 4 7 7 10 6 4 5 9 10 11 8 9 6 4 3 12 6 8

a. Specify the competing hypotheses to determine whether the ratings are significantly different between the tw o faculty members.

b. Calculate the value of the test statistic.

c. Determine the critical values at the 10% significance level.

d. Do the data suggest significantly different faculty ratings?