The sample data in the following Latin square are the scores obtained by nine college students of various ethnic backgrounds and various professional interests in an American history test:

In this table, A, B, and C are the three instructors by whom the nine college students were taught the course in American history. Analyze these data and test the following hypotheses at the 0.05 level of significance:
(a) Having a different instructor has no effect on the scores.
(b) Differences in ethnic background have no effect on the scores.
(c) Differences in professional interest have no effect on the scores.

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Ethnic background Mexican German Polish 86 79 83 Law 75 69 Medicine 95 Engineering 7083 93