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Problem-Solving and Data AnalysisEasy–MediumWhat a random sample allows you to generalise to

Problem-Solving and Data Analysis practice question

A researcher selected 300 employees at random from all 4,000 employees of a single company and surveyed them about their commute. Of those surveyed, 62% said they were satisfied with their commute.

Which conclusion is most appropriate?

  1. A. The result can reasonably be generalised to all 4,000 employees at that company.Correct
  2. B. The result can reasonably be generalised to all employees in the country.
  3. C. The result shows that a shorter commute causes higher job satisfaction.
  4. D. No conclusion can be drawn, because 300 is too small a number of people.

Answer: A. The result can reasonably be generalised to all 4,000 employees at that company.

The 300 employees were chosen at random from the company's 4,000 employees, so that company's workforce is the population the sample represents and the one the result can be generalised to.

Why the other answers are wrong

B. The result can reasonably be generalised to all employees in the country.
The random selection happened within one company. Nobody outside it had any chance of being surveyed, so the result says nothing reliable about employees elsewhere.
C. The result shows that a shorter commute causes higher job satisfaction.
The survey asked about satisfaction; it didn't assign anyone a commute or even compare commute lengths. No causal claim is available from it.
D. No conclusion can be drawn, because 300 is too small a number of people.
300 randomly chosen people out of 4,000 is a substantial sample. Small samples widen the margin of error — they don't make a random sample worthless.

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