Practice question · Numerical answer
Holding the confidence level fixed, by what factor must the sample size be multiplied to halve the margin of error?
Hints
- The margin is proportional to 1 over the square root of n.
- Doubling the square root of n requires what change in n?
Show the answer
4
Why
Halving the margin needs root n doubled, so n must be quadrupled. This square-root law is why polls quote margins of about 3 points at n = 1000: getting to 1.5 points would demand 4000 respondents.
Practise Confidence Intervals and Estimation
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