Question 7 • 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. This will allow the owner to expand the orchard. The owner takes a random sample of 30 apples and records their mean weight. What is the consequence of a Type I error in this situation?
Answer
A
The owner believes the crop will be more profitable and expands the orchard when the true mean weight of the apples is actually greater than 140 grams.
B
The owner believes the crop will not be more profitable and does not expand the orchard when the true mean weight of the apples is actually greater than 140 grams.
C
The owner believes the crop will be more profitable and expands the orchard when the true mean weight of the apples is actually not greater than 140 grams.
D
The owner believes the crop will not be more profitable and does not expand the orchard when the true mean weight of the apples is actually not greater than 140 grams.
Explanation
The null hypothesis is that the apples’ true mean weight is not greater than 140 grams; the alternative is that it is greater than 140 grams. A Type I error means rejecting the null when it is actually true. So the owner concludes the crop will be more profitable and expands the orchard even though the true mean weight is not greater than 140 grams, as choice C describes.
AI-written and checked against the verified answer.