Why use 0.5 for proportion?

When you do not know the expected proportion, 0.5 maximizes the variance (p x (1-p)), giving the most conservative sample size.

What if my population is very large?

For very large populations, the finite correction has minimal effect and the sample size approaches the infinite-population formula.

Higher confidence requires a larger sample. Going from 95% to 99% confidence increases sample size by about 75%.

Determine the minimum sample size needed for a research study based on confidence level, margin of error, and population proportion.

Z-Score for Confidence Level

1.645 = 90%, 1.96 = 95%, 2.576 = 99%

Margin of Error

As a decimal, e.g. 0.05 for 5%

Expected Proportion

0.5 gives the largest (most conservative) sample

Population Size

Leave large if unknown

Required Sample Size

370

Sample (Infinite Population)385

Required Sample Size vs Z-Score for Confidence Level

The sample size formula balances precision against cost. A larger sample reduces the margin of error but requires more resources.

n_0 = Z^2 x p x (1 - p) / E^2

With finite population correction:

n = n_0 / (1 + (n_0 - 1) / N)

Where Z is the z-score for your confidence level, p is the expected proportion, E is margin of error, and N is population size.

Using p = 0.5 gives the most conservative (largest) sample size when the true proportion is unknown.

A researcher needs 95% confidence (Z = 1.96), 5% margin of error, expected proportion 0.5, population 10,000.