Problem-Solving and Data AnalysisEasy–MediumSpotting a biased sampling method
Problem-Solving and Data Analysis practice question
A school newspaper wants to estimate the proportion of all students at the school who play a musical instrument. Which sampling method is most likely to give a biased estimate?
- A. Surveying students as they leave the band rehearsal roomCorrect
- B. Selecting 100 students at random from the school's enrolment list
- C. Surveying every tenth student entering the school in the morning
- D. Drawing 100 student ID numbers from a hat containing all of them
Answer: A. Surveying students as they leave the band rehearsal room
Students leaving band rehearsal are far more likely than average to play an instrument, so that sample overstates the proportion.
Why the other answers are wrong
- B. Selecting 100 students at random from the school's enrolment list
- A random draw from the full list is the standard unbiased method.
- C. Surveying every tenth student entering the school in the morning
- A systematic sample of all arriving students has no link to instrument playing.
- D. Drawing 100 student ID numbers from a hat containing all of them
- A random draw from all IDs is also fair.
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