Inference From Sample Statistics and Margin of Error
Estimating population values from samples and understanding margin of error
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You get a sample result and a margin of error. The question asks: what can you say about the whole population?
Why this matters
Inference questions test one idea: a sample tells you something about the population, but not exactly. The SAT gives you three variations of this concept. Students who understand estimation and margin of error individually still stumble when both show up together.
The three patterns
Estimation
Scale a sample proportion up to the full population. If 30% of 200 sampled say yes, estimate how many in 10,000 would say yes.
›Margin of Error
Build the plausible range: statistic ± margin of error. The true value likely falls somewhere in that interval.
›Estimate with Error
Combine both ideas. Scale up to the population and apply the margin of error to get a plausible range of actual counts.
The biggest trap: applying the margin of error to the sample instead of the population estimate. The margin of error defines a range for the true population value, not for your sample.