What this SAT skill is testing
Inference from a sample means using sample results to estimate something about a larger population. SAT questions focus on proportions, sample size, representative sampling, and margin of error.
A sample statistic is an estimate, not an exact population value. The margin of error describes a reasonable range around that estimate.
Key ideas
- A sample proportion is ( rac{ ext{number with the trait}}{ ext{sample size}}).
- An estimated population count is (( ext{sample proportion})( ext{population size})).
- An estimate of (p%) with margin of error (m) percentage points gives the interval from (p-m) to (p+m).
- Larger random samples usually produce smaller margins of error.
- A larger sample does not fix a biased selection method.
Worked SAT-style example
In a random sample of 400 voters, 52% support a proposal. The margin of error is 4 percentage points.
The plausible interval is (52%-4%=48%) to (52%+4%=56%). A claim that exactly 52% of all voters support the proposal is too strong. A claim that population support could reasonably be 50% is consistent with the interval.
Estimating a population count
If 18% of a representative sample has a certain response and the population contains 2,500 people, the estimated count is (0.18(2500)=450). Because this is an estimate, the wording should not imply that exactly 450 people have that response.
Step-by-step method
- Identify the population the question asks about.
- Confirm that the sample can reasonably represent that population.
- Convert the sample result to a proportion or percent.
- Apply the proportion to the population, or build the margin-of-error interval.
- Choose a conclusion whose certainty matches the data.
Common traps
- Adding 4% of the estimate when the problem says 4 percentage points.
- Using the population size as the denominator for a sample proportion.
- Treating the endpoints of an interval as impossible cutoffs rather than plausible bounds.
- Assuming a result from one city represents an entire country.
- Thinking that doubling the sample automatically removes all bias.
How to practice efficiently
For each question, write one of three setups before calculating: sample proportion, population estimate, or estimate ± margin of error. Most SAT questions in this unit reduce to one of those patterns.
