Optional extension: Stratification, capture–recapture and sample precision
Example 1
For this model, margin of error E=√nc, with fixed c. A sample of 225 gives margin 36. Find the smallest whole-number sample size that gives a margin of at most 30.
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Answer: 324
- From E ∝ √n1, the required n is at least 225×(3036)2=324.
- Round up to 324.
Example 2
The two strata were sampled at different rates. Using each stratum's observed support rate, estimate the population-wide support percentage. Give an exact fraction if needed.
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Answer: 4155
- A's estimated supporters =300×306;
- B's =500×10050.
- Add these estimates, divide by population 800
- multiply by 100.
- Do not pool the unequal-rate samples directly.
Example 3
For this model, margin of error E=√nc, with fixed c. A sample of 100 gives margin 15. Find the smallest whole-number sample size that gives a margin of at most 10.
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Answer: 225
- From E ∝ √n1, the required n is at least 100×(1015)2=225.
- Round up to 225.