Problem-Solving and Data AnalysisVery hardDistribution of many sample means
Problem-Solving and Data Analysis practice question
A researcher draws 1,000 random samples of 50 adults each from a population and records the mean height of each sample. Compared with the heights of individual adults in the population, the 1,000 sample means are ____
- A. centred at about the same value but much less spread out.Correct
- B. centred at a higher value and more spread out.
- C. centred at about the same value and equally spread out.
- D. centred at a lower value and less spread out.
Answer: A. centred at about the same value but much less spread out.
Averaging 50 heights pulls each sample mean toward the population mean.
Why the other answers are wrong
- B. centred at a higher value and more spread out.
- Averaging does not shift the centre upward.
- C. centred at about the same value and equally spread out.
- Means of 50 vary much less than single heights.
- D. centred at a lower value and less spread out.
- Averaging does not shift the centre downward.
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