From previous experience, the owner of an apple orchard knows that the mean weight of Gala apples is 140 grams. There has been more precipitation than usual this year. The owner believes the weights of the apples will be heavier than usual and therefore the crop will be more profitable. The owner takes a random sample of 30 apples and records their mean weight. What is a Type II error in this situation?
Answer
A
Based on the sample mean, the owner concludes that the mean weight of apples is not greater than 140 grams when the true mean weight is not greater than 140 grams.
B
Based on the sample mean, the owner concludes that the mean weight of apples is greater than 140 grams when the true mean weight is not greater than 140 grams.
C
Based on the sample mean, the owner concludes that the mean weight of apples is greater than 140 grams when the true mean weight is greater than 140 grams.
D
Based on the sample mean, the owner concludes that the mean weight of apples is not greater than 140 grams when the true mean weight is greater than 140 grams.
Explanation
The owner is testing whether the true mean apple weight is greater than 140 grams. A Type II error occurs when the true mean is greater than 140 grams, but the sample does not provide enough evidence for the owner to conclude that it is greater than 140 grams. That matches choice D: concluding the mean is not greater than 140 grams when it actually is.
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