Problem-Solving and Data AnalysisHardWhich sample mean to trust more
Problem-Solving and Data Analysis practice question
Two random samples of households were taken from the same town to estimate the town's mean weekly grocery spending. Sample 1 had 100 households and a mean of $141. Sample 2 had 400 households and a mean of $139. Which sample's mean is more likely to be close to the town's true mean, and why?
- A. Sample 2, because a larger random sample has less sampling variability.Correct
- B. Sample 1, because its mean is higher.
- C. Sample 1, because a smaller sample is easier to measure accurately.
- D. Neither, because the two means are different.
Answer: A. Sample 2, because a larger random sample has less sampling variability.
Larger random samples give estimates that vary less from the population value.
Why the other answers are wrong
- B. Sample 1, because its mean is higher.
- A higher mean is not a more accurate one.
- C. Sample 1, because a smaller sample is easier to measure accurately.
- Ease of measurement does not reduce sampling variability.
- D. Neither, because the two means are different.
- Sample means always differ a little; the larger sample is still more reliable.
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