Three different 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:

Opinion

Commercial 1 2 3 4 5 Total

A 32 87 91 46 44 300

B 53 141 76 20 10 300

C 41 93 67 36 63 300

Total 126 321 234 102 117 900

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 for the opinion distributions are different for the variouscommercials? Useα= 0.1.