How many trials to poll a proportion

You will estimate a proportion whose true value is around p=0.5p = 0.5. You need the standard error of p^\hat p to be at most 0.020.02. What is the smallest number of independent trials nn that achieves this?

Show hints (2)+
  1. Set sqrt(p(1-p)/n) <= 0.02 and square both sides to free n.
  2. With p(1-p) = 0.25, n >= 0.25 / 0.02^2.

Answer

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625

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