A market research study was conducted to compare three diffe

A market research study was conducted to compare three different brands of antiperspirant. The results of the study are summarized below. Use a 5% level of significance and test the claim that opinion is independent of brand. Use these data to answer questions 12 and 13.

Brand

Opinion

A

B

C

Total

Excellent

29

37

50

116

Satisfactory

83

65

83

231

Unsatisfactory

18

9

6

33

Total

130

111

139

380

What is your conclusion?

A.Opinion and brand are independent

B.Opinion and brand are not independent

C.Cannot determine

Solution

expected: contingency table

A B C

1 39.7 33.9 42.4
2 79.0 67.5 84.5
3 11.3 9.64 12.1



chi-square = 11.9
degrees of freedom = 4
probability = 0.018
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What is the value of the sample test statistic?
Answer: D. X2 = 11.91
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What is your conclusion?
Answer: B. Opinion and brand are not independent