Problem-Solving and Data AnalysisHardComparing two estimates with margins of error
Problem-Solving and Data Analysis practice question
Two random samples estimate the proportion of defective parts from two machines. Machine A: 4% ± 1%. Machine B: 6% ± 3%. Which conclusion is most appropriate?
- A. Machine A's defect rate is estimated more precisely, and the two intervals overlap, so the data do not establish which machine has the higher rate.Correct
- B. Machine B definitely has the higher defect rate.
- C. The two machines have exactly the same defect rate.
- D. Machine A's sample must have been smaller than Machine B's.
Answer: A. Machine A's defect rate is estimated more precisely, and the two intervals overlap, so the data do not establish which machine has the higher rate.
A's interval is 3%–5%; B's is 3%–9%. They overlap, and A's is narrower.
Why the other answers are wrong
- B. Machine B definitely has the higher defect rate.
- Overlapping intervals do not settle which rate is higher.
- C. The two machines have exactly the same defect rate.
- Overlap doesn't prove equality.
- D. Machine A's sample must have been smaller than Machine B's.
- A smaller margin usually means a LARGER sample.
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