16Hit1600
Problem-Solving and Data AnalysisVery hardComparing two intervals that overlap

Problem-Solving and Data Analysis practice question

Two random samples of the same size were taken from two lakes. The mean length of fish in Lake A was estimated as 24 cm with a margin of error of 3 cm; in Lake B, 28 cm with a margin of error of 3 cm. Which of the following is the most appropriate conclusion?

  1. A. The mean length in Lake B is probably greater than in Lake A, but the intervals overlap, so the samples do not establish the difference conclusively.Correct
  2. B. Every fish in Lake B is longer than every fish in Lake A.
  3. C. The two lakes have the same mean fish length.
  4. D. The mean length in Lake A is exactly 24 cm.

Answer: A. The mean length in Lake B is probably greater than in Lake A, but the intervals overlap, so the samples do not establish the difference conclusively.

Interval A is 21–27, interval B is 25–31. They overlap (25–27), so the difference is suggested, not settled.

Why the other answers are wrong

B. Every fish in Lake B is longer than every fish in Lake A.
Margins of error are about MEANS, not individual fish.
C. The two lakes have the same mean fish length.
Overlap doesn't prove equality; the estimates differ by 4 cm.
D. The mean length in Lake A is exactly 24 cm.
24 is an estimate with a ±3 margin, not an exact value.

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