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 apples. If the farmer had selected 160 trees from his large apple orchard rather than 40 trees, what effect would this have had on the margin of error?
Answer
A
It would have doubled.
B
It would have been cut in half.
C
It would have remained the same.
D
It would be larger, but it would not have doubled.
Explanation
For the same confidence level, the margin of error is proportional to 1/√n, where n is the sample size. Increasing the sample from 40 to 160 quadruples it, so the margin of error is multiplied by 1/√4 = 1/2. Therefore, it would have been cut in half.
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