After a product recall, a company solicits feedback from a random sample of 100 customers regarding their opinion about the company since the recall. Customers were asked, "Do you approve, disapprove, or have no opinion about the company?” The public relations department is concerned that the opinions may be equally distributed across these three options. The survey reveals that 38 customers approve, 45 disapprove, and 17 have no opinion. They decide to carry out a test of the following hypotheses:H0: Customer opinion is equally distributed across the three options.Ha: Customer opinion is not equally distributed across the three options.
Answer
A
Reject H0. There is convincing evidence that the distribution of customer opinion is equally distributed across the three options.
B
Reject H0. There is convincing evidence that the distribution of customer opinion is not equally distributed across the three options.
C
Fail to reject H0. There is convincing evidence that the distribution of customer opinion is equally distributed across the three options.
D
Fail to reject H0. There is convincing evidence that the distribution of customer opinion is not equally distributed across the three options.
Explanation
If opinions are equally distributed, the expected count is 100 ÷ 3 ≈ 33.3 in each category. The chi-square statistic is (38 − 33.3)²/33.3 + (45 − 33.3)²/33.3 + (17 − 33.3)²/33.3 ≈ 13.07, with 2 degrees of freedom; this gives a p-value of about 0.001. Since that is strong evidence against equal distribution, reject H0. Choice B correctly concludes that customer opinion is not equally distributed.
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