A yogurt company claims that it prints a free yogurt coupon under a randomly selected 20% of its lids. A loyal customer purchases 85 yogurt cups, and records whether each was a winner. After consuming all 85 cups, he is disappointed to see that only 12 (14.1%) of his yogurt cups contained coupon codes. He performs a 99% confidence interval for the proportion of yogurt cups containing coupon codes, obtaining (0.044, 0.238). What conclusion can the customer draw about the yogurt company’s claim?
Answer
A
The company’s claim may be justified because 0.2 is in the confidence interval.
B
The company’s claim is definitely justified because 0.2 is in the confidence interval.
C
The company’s claim is not justified because the upper endpoint of the confidence interval is 0.238.
D
The company’s claim is not justified because 12 out of 85 (0.141) is far less than 0.2.
Explanation
The 99% confidence interval, (0.044, 0.238), includes 0.20, the proportion claimed by the company. Thus the data are consistent with the claim, so the claim may be justified. The interval does not prove the claim is true, which is why “definitely justified” is too strong.
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