Margin of error and statistical claims
These questions give you a result, a margin of error, and four conclusions. Three of them claim more than the data can support. The skill is spotting which extra step each wrong conclusion takes.
The interval is the whole idea
A survey finds 54% support with a margin of error of 3 percentage points. That does not mean the truth is 54%. It means plausible values run from 51% to 57%, and every supported conclusion has to fit inside that range. A claim about more than half is supported when the whole interval sits above 50%, not when 54 does.
Sample size moves the margin
A larger random sample narrows the margin of error, which tightens the interval. A smaller sample widens it. What sample size cannot fix is how the sample was chosen: a large biased sample is still biased, and a narrow interval built on a biased sample is a precise wrong answer.
Random selection buys generalisation
A conclusion may describe the population the sample was randomly drawn from. It cannot describe individuals. If a survey says the average commute is 32 minutes, that is a statement about the group, not a promise that your commute is 32 minutes. It also cannot describe a wider population than the one sampled.
Random assignment buys causation
An experiment randomly assigns the treatment, and that assignment is what lets a conclusion say the treatment caused the result. An observational study only watches what people already do. It can show an association, and an association is not a cause, no matter how large or consistent the sample.
The three claim traps
Almost every wrong answer is one of these in a costume. Read each option and name the extra step it takes, because the step is the error.
- A claim about every individual instead of the population
- A causal claim from an observational study
- A conclusion about a wider population than the sample represents
- An exact value where only an interval was earned
A four-question habit
Before choosing, ask four things in order: was the sample random, was the treatment randomly assigned, what population does the sample stand for, and does the interval actually contain the claim. Ninety seconds of that routine resolves most of these questions, and it also tells you when an option is right for a reason you can explain rather than recognise.
What does margin of error mean on the SAT?
A range around the sample result where the population value plausibly sits, written as plus or minus a number of percentage points. A result of 54% with a margin of error of 3 points means 51% to 57%.
Does a bigger sample always mean a better study?
It narrows the margin of error, but a large biased sample is still biased. Random selection is what allows a conclusion to generalise, and sample size only sharpens the estimate.
When can a study support a cause?
When the researchers randomly assigned who received the treatment. That is the line between an experiment and an observational study, and it is the line the causal answer choices are testing.
Can a survey prove that most people prefer something?
It can support that conclusion when the whole interval sits above half. If the interval straddles 50%, the data is compatible with both a majority and a minority.
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