š Math
Sample Size Calculator
Determine the minimum sample size required for a survey or experiment to achieve statistically significant results. Considers population size, confidence level, and margin of error.
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Formula
n = (ZĀ² Ć p Ć (1-p)) / EĀ²n- Required sample size
Z- Z-score for your confidence level (e.g., 1.96 for 95%)
p- Expected population proportion (default to 0.5 for max size)
E- Margin of Error (as a decimal)
Example
Sizing a Political Poll
Find the sample size needed for a 95% confidence level and 5% margin of error in a very large population.
- Set Z = 1.96 (for 95% confidence), E = 0.05, and p = 0.5.
- Calculate numerator: 1.96Ā² Ć 0.5 Ć (1-0.5) = 3.8416 Ć 0.25 = 0.9604.
- Calculate denominator: 0.05Ā² = 0.0025.
- Divide: 0.9604 / 0.0025 = 384.16.
- Result: Round up to the nearest whole person, requiring 385 people.
Frequently Asked Questions
Setting the expected proportion (p) to 0.5 maximizes the numerator of the formula, guaranteeing that the calculated sample size will be large enough regardless of what the true proportion turns out to be. It is the most conservative estimate.