Calculate the required sample size for a given population size and margin of error.
Required Sample Size (n):
Understanding Slovin's Formula
Slovin's formula is used to determine the minimum sample size required to estimate a population proportion with a given margin of error. This formula is especially useful when dealing with large populations where surveying everyone would be impractical.
Formula
$$ n = \frac{N}{1 + N \cdot e^2} $$
- N: Population size
- e: Desired margin of error, expressed as a decimal (e.g., 0.05 for 5%)
- n: Sample size needed to achieve the desired precision
Example Calculation
Suppose a researcher wants to estimate the proportion of people in a city of 10,000 residents who support a new policy, with a margin of error of 5%.
- Step 1: Population size \( N = 10000 \)
- Step 2: Margin of error \( e = 5\% = 0.05 \)
- Step 3: Apply Slovin's formula: \[ n = \frac{10000}{1 + 10000 \cdot 0.05^2} \approx 385 \]
The researcher needs a sample size of approximately 385 to estimate the proportion with a 5% margin of error.