For scholarship purposes, two 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 following table.

a. Using the sign test, specify the competing hypotheses to determine whether the ratings differ between the two faculty members.
b. Determine the critical value(s) at the 10% significance level.
c. Calculate the value of the test statistic.
d. Do the data suggest that faculty ratings differ? Explain.

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Faculty Faculty Faculty Faculty B's A's A's B's Candidate Rating Rating Candidate Rating Rating 10 100 10 12