Three different television commercials are advertising an established product. The ­commercials are shown separately to theater panels of consumers; each consumer views only one of the possible commercials and then states an opinion of the product. Opinions range from 1 (very favorable) to 5 (very unfavorable). The data are as follows.

a. Calculate expected frequencies under the null hypothesis of independence.
b. How many degrees of freedom are available for testing this hypothesis?
c. Is there evidence that the opinion distributions are different for the various commercials? Use a = .01.

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Opinion Commercial 45 Total 3 32 87 9 464 300 53 141 7 2010 300 41 93 67 3663 300 Total 126 32 234 102 7 900