Question 8 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
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 I error in this situation?
Answer
A
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.
B
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.
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 of the apples 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 of the apples is greater than 140 grams.
Explanation
The owner's claim is that the population mean weight is greater than 140 grams, so the alternative hypothesis is that μ > 140. A Type I error means rejecting the null hypothesis when it is true: the owner concludes the mean is greater than 140 grams even though the true mean is not greater than 140 grams. That is choice A.
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