Problem-Solving and Data AnalysisHardTwo sample means from one population
Problem-Solving and Data Analysis practice question
Two random samples of 100 people are drawn from the same city. The first has a mean age of 52 years and the second a mean age of 48 years. Which of the following statements is best supported?
- A. Both means are estimates of the city's mean age, which is plausibly near 50; the difference reflects sampling variability.Correct
- B. The city's mean age changed between the two samples.
- C. One of the samples must have been chosen incorrectly.
- D. The city's mean age is exactly 50.
Answer: A. Both means are estimates of the city's mean age, which is plausibly near 50; the difference reflects sampling variability.
Different random samples give different estimates of the same value.
Why the other answers are wrong
- B. The city's mean age changed between the two samples.
- Nothing suggests the population changed.
- C. One of the samples must have been chosen incorrectly.
- Random samples differ by chance.
- D. The city's mean age is exactly 50.
- 50 is plausible, not exact.
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