Conducting a Chi-Square Test for Goodness of Fit — Quiz
Question 4 • Statistics
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. They decide to carry out a test of significance. What are the appropriate hypotheses?
Answer
A
cap h sub 0 : Approximately 33 customers approve, approximately 33 disapprove, and approximately 33 customers have no opinion of the company. cap h sub A : At least one of these values differs from those stated in the null hypothesis.
B
cap h sub 0 : Customer opinion is not equally distributed across the three options. cap h sub A : Customer opinion is equally distributed across the three options.
C
cap h sub 0 : Customer opinion is equally distributed across the three options. cap h sub A : Customer opinion is not equally distributed across the three options.
D
cap h sub 0 : Approximately 34 customers approve, approximately 34 disapprove, and approximately 34 customers have no opinion of the company. cap h sub A : At least one of these values differs from those stated in the null hypothesis.
Explanation
For a goodness-of-fit test, the null hypothesis states the expected population distribution. Here, that means customer opinions are equally distributed among approve, disapprove, and no opinion, with one-third in each category. The alternative is that the distribution is not equal; choice C states these hypotheses. The hypotheses concern proportions, not exact sample counts such as 33 or 34 out of 100.
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