Margin of error
SAT glossary · Math
Definition
The half-width of a confidence interval, scaling as 1/√(n). Halving it requires quadrupling the sample size - the relationship tested in study-design items.
Margin of error in plain English
Margin of error tells you how much 'wiggle room' to expect around a survey's estimate, and it shrinks as your sample size n grows — but not proportionally. It actually shrinks in proportion to frac1√(n) (one over the square root of your sample size), which means to cut your margin of error exactly in HALF, you can't just double your sample — you need to QUADRUPLE it (multiply it by 4), because √(4)=2. This relationship between sample size and precision is exactly what study-design questions are testing when they ask how much bigger a sample needs to be to hit a certain precision target.
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