Practice question · Multiple choice
Polls typically sample around a thousand people whether the population is a city or a country of 60 million. Why does population size barely matter?
Hints
- Write the standard error formula. Does the population size appear in it?
- A cook tastes one spoonful whether the pot holds a litre or a hundred. Why does that work?
Show the answer
C. Because the standard error depends on sample size, not on the fraction
Why
The formula contains n and not N, so what matters is how many you asked rather than what fraction they represent, the soup only needs to be stirred. The intuition that a bigger country needs a bigger poll is among the most persistent errors about sampling, and it is simply not in the mathematics.
Practise Sampling and the Central Limit Theorem
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