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Math · 11 · Problem-Solving and Data Analysis · Free

Surveys

Notes

Key points

  • Random sampling → results generalise to the population sampled, and only that one.
  • Random assignment to treatments → cause-and-effect conclusions are allowed.
  • Observational study (no assignment) → association only, never causation.
  • Biased samples: volunteers, convenience groups, one website's users → can't generalise.
  • Estimate ± margin of error = the plausible range for the population value.
  • Larger sample → smaller margin of error. More variability → larger margin.

Formulas

Sample proportionp^=number with traitsample size\hat{p}=\dfrac{\text{number with trait}}{\text{sample size}}
Plausible intervalestimate±margin of error\text{estimate}\pm\text{margin of error}
Population estimatep^×population size\hat{p}\times\text{population size}

Common traps

  • Claiming causation from a study where subjects chose their own group.
  • Generalising from one school, town or club to everyone.
  • Treating the margin of error as a guarantee — values outside are just unlikely.

SAT tip

Ask two questions: was the sample random (generalise?) and were treatments randomly assigned (cause?). The answer choice follows.

Test yourself

10 official SAT questions on Surveys, easiest first.

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