Problem-Solving and Data AnalysisVery hardGeneralising to the right population
Problem-Solving and Data Analysis practice question
A researcher wants to estimate the mean daily commute time of adults in a certain state. She surveys 600 adults selected at random from the residents of the state's largest city. Which of the following is the most appropriate statement about her estimate?
- A. It can reasonably be generalised to adults in that city, but not reliably to adults across the state.Correct
- B. It can reasonably be generalised to all adults in the state, because 600 is a large sample.
- C. It cannot be generalised to any group, because the sample was not selected from the whole state.
- D. It is exact for adults in that city, because the sample was selected at random.
Answer: A. It can reasonably be generalised to adults in that city, but not reliably to adults across the state.
Random selection lets a sample speak for the population it was drawn FROM. That population is the city's residents, whose commutes may differ from those elsewhere in the state.
Why the other answers are wrong
- B. It can reasonably be generalised to all adults in the state, because 600 is a large sample.
- A large sample makes an estimate more precise, but it can't fix the mismatch between the sampled population (one city) and the target (the whole state).
- C. It cannot be generalised to any group, because the sample was not selected from the whole state.
- The sample WAS randomly selected from the city, so generalising to the city's adults is sound.
- D. It is exact for adults in that city, because the sample was selected at random.
- A random sample gives an estimate with a margin of error, never an exact population value.
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