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A school sends a survey about the canteen to the parents of 1500 students, chosen as the whole…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A school sends a survey about the canteen to the parents of 1500 students, chosen as the whole school. It gets 420 forms back. Of the returned forms, 63% complain about the food. Find the response rate. Then explain why the 63% may not describe all the parents.
Need a reminder? The key ideaShow
When two groups reply at different rates and , the share of the first group among the replies is . A larger sample shrinks the luck, about percentage points, but never the bias.
The worked solution
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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The response rate. .
Step 2. Why it may mislead. Fewer than one parent in three replied. Parents who are unhappy are more likely to take the trouble to write. So the 63% probably overstates the complaints. This is non-response bias.
Answer: . The parents who replied may not be like the parents who did not.
What if? The school could follow up a small random sample of the parents who did not reply. If they complain much less, the 63% is too high.
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