Problem-Solving and Data AnalysisHardEffect of a larger sample on the interval
Problem-Solving and Data Analysis practice question
A researcher estimates the mean weight of apples in an orchard from a random sample of 50 apples and reports a margin of error of 12 grams. She then repeats the study with a random sample of 200 apples from the same orchard. Which of the following is most likely true about the second study?
- A. Its margin of error is smaller than 12 grams.Correct
- B. Its margin of error is larger than 12 grams.
- C. Its margin of error is exactly 12 grams.
- D. Its sample mean is exactly the orchard's true mean.
Answer: A. Its margin of error is smaller than 12 grams.
A larger random sample gives a more precise estimate, so the margin of error shrinks (quadrupling the sample roughly halves it).
Why the other answers are wrong
- B. Its margin of error is larger than 12 grams.
- More data does not make an estimate less precise.
- C. Its margin of error is exactly 12 grams.
- The margin of error depends on sample size, so it changes.
- D. Its sample mean is exactly the orchard's true mean.
- A sample mean is still an estimate; no sample size makes it exactly the true mean.
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