Preparing to Conduct a Chi-Square Test for Goodness of Fit — Quiz
Question 3 • Statistics
As products come off a large assembly line, they are inspected for quality. They are placed into one of three categories: pass, fail, or need additional inspection. The manager claims that 80 percent of the products pass the inspection, 5 percent fail, and 15 percent need additional inspection. In an effort to increase the passing rate, the machines are recalibrated. After this recalibration, a random sample of 100 products is selected. The manager would like to know if there is convincing evidence that the distribution has changed. What are the appropriate hypotheses?
Answer
A
cap h sub 0 : p sub pass is equal to 0 point 8 0 , p sub fail is equal to 0 point 0 5 , p sub inspection is equal to 0 point 1 5 cap h sub A : Not all of the p sub i's are as stated.
B
cap h sub 0 : p sub pass is equal to 0 point 8 0 , p sub fail is equal to 0 point 0 5 , p sub inspection is equal to 0 point 1 5 cap h sub A : p sub pass is greater than 0 point 8 0 , p sub fail is less than 0 point 0 5 , p sub inspection is not equal to 0 point 1 5
C
cap h sub 0 : p sub pass is equal to 0 point 8 0 , p sub fail is equal to 0 point 0 5 , p sub inspection is equal to 0 point 1 5 cap h sub A : p sub pass is not equal to 0 point 8 0 , p sub fail is not equal to 0 point 0 5 , p sub inspection is not equal to 0 point 1 5
D
cap h sub 0 : p sub pass is equal to 0 point 8 0 , p sub fail is equal to 0 point 0 5 , p sub inspection is equal to 0 point 1 5 cap h sub A : p sub pass is greater than 0 point 8 0 , p sub fail is less than 0 point 0 5 , p sub inspection is less than 0 point 1 5
Explanation
The null hypothesis states that the category probabilities remain at the manager’s claimed values: 0.80 pass, 0.05 fail, and 0.15 need additional inspection. Because the question asks whether the distribution has changed, the alternative is that at least one of these probabilities differs from its claimed value. The manager’s goal of increasing the passing rate does not make this a one-directional test, since the question asks about any change.
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