Preparing to Conduct a Chi-Square Test for Goodness of Fit — Quiz
Question 6 • Statistics
A manufacturer of large kitchen appliances keeps track of the costs of warranty claims. Management suspects that 75 percent of all warranty claims are invalid, 20 percent cost the company less than 500 dollars , and 5 percent of them cost the company more than 500 dollars To investigate this belief, a random sample of 80 warranty claims is selected from their vast records of past warranty claims. The management would like to know if the distribution of claim results differs from what they suspect. Are the conditions for inference met?
Answer
A
No, the 10 percent condition is not met.
B
No, the random condition is not met.
C
Yes, all of the conditions for inference are met.
D
No, the Large Counts condition is not met.
Explanation
For a chi-square goodness-of-fit test, each expected count should be at least 5. With 80 claims, the expected counts are 0.75 × 80 = 60 invalid claims, 0.20 × 80 = 16 claims costing less than $500, and 0.05 × 80 = 4 claims costing more than $500. Since 4 is below 5, the Large Counts condition is not met, so choice D is correct.
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