Problem-Solving and Data AnalysisVery hardComparing precision of two estimates
Problem-Solving and Data Analysis practice question
Two random samples estimate the mean height of trees in two woods. Wood P: mean 14.0 m, margin of error 0.5 m, from 400 trees. Wood Q: mean 14.6 m, margin of error 2.0 m, from 25 trees. Which statement is most appropriate?
- A. Wood P's mean is estimated more precisely, and because the intervals overlap the data do not establish which wood has taller trees on average.Correct
- B. Wood Q's trees are definitely taller on average.
- C. The two woods have exactly the same mean height.
- D. Wood Q's estimate is more precise because its mean is larger.
Answer: A. Wood P's mean is estimated more precisely, and because the intervals overlap the data do not establish which wood has taller trees on average.
P's interval is 13.5–14.5; Q's is 12.6–16.6. They overlap, and P's is narrower.
Why the other answers are wrong
- B. Wood Q's trees are definitely taller on average.
- Overlapping intervals do not settle which is taller.
- C. The two woods have exactly the same mean height.
- Overlap doesn't prove equality.
- D. Wood Q's estimate is more precise because its mean is larger.
- Precision depends on the margin, which is larger for Q.
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