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 significance to determine if there is convincing evidence that the distribution of opinion in the population is equally distributed across the three options. What is the value of the chi-square test statistic and the cap p -value of this test? Use the chi-square distribution table.
Answer
A
chi squared is equal to 12 point 7 1 , cap p -value is between 0 point 0 0 1 and 0 point 0 0 2
B
chi squared is equal to 8 point 5 4 , cap p -value is between 0 point 0 1 and 0 point 0 2
C
chi squared is equal to 8 point 5 4 , cap p -value is between 0 point 0 2 5 and 0 point 0 5
D
chi squared is equal to 12 point 7 1 , cap p -value is between 0 point 0 5 and 0 point 1 0
Explanation
If opinions are equally distributed, the expected count in each category is 100 ÷ 3 ≈ 33.33. The chi-square statistic is (38 − 33.33)²/33.33 + (45 − 33.33)²/33.33 + (17 − 33.33)²/33.33 ≈ 12.71. There are 3 − 1 = 2 degrees of freedom; the chi-square table places this statistic’s p-value between 0.001 and 0.002. Thus, the matching choice is A: χ² = 12.71 and the p-value is between 0.001 and 0.002.
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