Survey margin of error and confidence interval.
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Margin of error = z × √(p(1−p)/n). Bigger samples shrink it; it's largest at p = 50%. We also give the confidence interval around your result.
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z × √(p(1−p)/n) for the chosen confidence level.
The margin of error is maximized at a 50/50 split.
Yes — it shrinks the margin (by √n).
Random sampling from a large population.