A sample estimate is not an exact population value. Keep the margin of error and the sampled population attached to the claim.
Sample statistics estimate features of a population. A margin of error describes uncertainty around an estimate under the stated method; it does not make the estimate an exact value or fix a biased sampling design.
Worked example: read the reported interval
All examples here are original teaching exercises, not released SAT questions. A random sample of adults in a city gives an estimated support rate of 62%, with a margin of error of 3 percentage points at a 95% confidence level. The reported interval is 59% to 65%.
The estimate does not establish that exactly 62% of every adult supports the proposal. A value of 64% is inside the reported interval, while 70% is outside. The interval represents uncertainty at the stated confidence level; it is not a guarantee that the population value lies inside it.
If the margin is written as 0.03 for a proportion, it corresponds to 3 percentage points. It is not 3% of 62%, which would use the wrong base.
Worked example: compare precision
Two surveys using comparable methods at the same confidence level report estimates of 48% ± 4 percentage points and 49% ± 2 percentage points. The second has a narrower interval, 47%–51% rather than 44%–52%, and therefore greater reported precision.
The intervals overlap. Their small difference in point estimates alone does not establish a population change. Conversely, overlap by itself is not a complete formal significance test. Follow the comparison the question actually asks you to make.
Sample size and sampling bias are different issues
With other features held comparable, larger random samples tend to reduce margin of error. That does not mean any larger sample is more representative. A voluntary poll on a cycling club's website may overrepresent cycling enthusiasts even if thousands respond.
A random sample drawn only from the cycling club can support estimates about that club's members under the sampling assumptions; it does not automatically describe all city residents. Keep the sampling frame attached to the conclusion.
Do not add a formula the question does not require
The SAT skill includes interpreting sample statistics and margin of error. Begin with the estimate, the supplied margin, the population, and the claim. A problem giving a margin does not require inventing a confidence level or calculating a normal-distribution critical value.
If a question supplies a relationship between sample size and margin, use that relationship with its assumptions. Precision, representativeness, and causation are separate issues; a narrow interval does not turn an observational survey into an experiment.
A four-question check
- What population was sampled?
- What was estimated, in which unit?
- What uncertainty was reported?
- Does the proposed claim stay within those limits?
For claims about causation or wider populations, continue to observational studies and experiments. Record whether an error came from the interval arithmetic, the units, the population, or an overstated conclusion.
Official sources
Next step