Find the sample size that produces the margin of error ± 3.0%
To find the sample size that produces a margin of error of ±3.0%, we need to use the following formula:
n = (Z * σ / E)^2
Where:
- n is the required sample size
- Z is the desired Z-score for a given confidence level
- σ is the standard deviation of the population (if known)
- E is the margin of error
Since we haven't been provided with a specific confidence level or the standard deviation of the population, we will assume a 95% confidence level and use a conservative estimate for the standard deviation of the population at 0.5. You can adjust these values according to your specific scenario.
Therefore, using Z = 1.96 (for a 95% confidence level) and E = 0.03 (3.0% margin of error), we can calculate the sample size as follows:
n = (1.96 * 0.5 / 0.03)^2
Simplifying the equation:
n ≈ (98 / 0.03)^2
n ≈ 32345.68
Therefore, the sample size required to generate a margin of error of ±3.0% (at a 95% confidence level, using a standard deviation estimate of 0.5) is approximately 32,346.