A farmer of a large apple orchard would like to estimate the true mean number of suitable apples produced per tree. He selects a random sample of 40 trees from his large orchard and determines with 95% confidence that the true mean number of suitable apples produced per tree is between 375 and 520. Which of these statements is a correct interpretation of the confidence level?
Answer
A
Approximately 95% of the trees in the orchard contain between 375 and 520 suitable apples.
B
There is a 95% probability that the true mean number of apples per tree is between 375 and 520.
C
If many random samples of size 40 are selected from the population of all trees in this large orchard, approximately 95% of the sample means will be between 375 and 520 apples.
D
If many random samples of size 40 are selected from the population of all trees in this large orchard, about 95% of the intervals would capture the true mean number of suitable apples produced per tree.
Explanation
A 95% confidence level describes how well the interval-making method works over repeated samples. If many random samples of 40 trees were taken and an interval were calculated from each sample, about 95% of those intervals would contain the orchard’s true mean number of suitable apples per tree. It does not mean that 95% of individual trees fall in the interval or that the fixed true mean has a 95% probability of being there.
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