Samples, studies and margin of error

Digital SAT · Math · Problem-Solving and Data Analysis. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

These questions have little arithmetic. They ask what you are allowed to conclude from a study. Check two things: how the people were chosen, and how they were put into groups.

If the sample was chosen at random, the result can be applied to the whole population the sample came from, and to no wider group. If the people were randomly assigned to a treatment, the study is an experiment and can show cause and effect. A study that only observes people can show a link, not a cause.

A sample result is only an estimate. The margin of error gives a range around it where the true population value plausibly lies.

Rules to remember

Common mistake

Saying that everyone, or a fixed share of individuals, falls inside the margin of error. The range describes the plausible value of the population mean or percent, and nothing about single members.

Worked example

In a random sample of 500 of the 20,000 residents of a town, 30% said they use the bus each week. The margin of error is 4%. What is a plausible range for the number of residents of the town who use the bus each week?

  1. Plausible percent: 30% − 4% = 26% to 30% + 4% = 34%.
  2. Lower number: 0.26 × 20,000 = 5,200.
  3. Upper number: 0.34 × 20,000 = 6,800.

Answer: Between 5,200 and 6,800 residents

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