How To Calculate A Sample Size From A Population

Finite Population Sample Size Formula:

\[ n = \frac{N Z^2 p (1-p)}{E^2 (N-1) + Z^2 p (1-p)} \]

Population Size (N):

units

Z-Score (Z):

unitless

Proportion (p):

unitless

Margin of Error (E):

unitless

Sample Size (n):

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1. What is the Finite Population Sample Size Formula?

The finite population sample size formula calculates the required sample size when sampling from a finite population. It provides a more accurate estimate than the infinite population formula when the sample represents a significant portion of the total population.

2. How Does the Calculator Work?

The calculator uses the finite population sample size formula:

\[ n = \frac{N Z^2 p (1-p)}{E^2 (N-1) + Z^2 p (1-p)} \]

Where:

\( n \) — Required sample size (unitless)
\( N \) — Total population size (units)
\( Z \) — Z-score for desired confidence level (unitless)
\( p \) — Estimated proportion (unitless)
\( E \) — Margin of error (unitless)

Explanation: This formula adjusts for finite population correction, providing more precise sample size estimates when sampling from smaller populations.

3. Importance of Sample Size Calculation

Details: Proper sample size calculation ensures research studies have adequate statistical power, minimizes sampling error, and provides reliable results that can be generalized to the entire population.

4. Using the Calculator

Tips: Enter population size as a positive integer, Z-score based on confidence level (1.96 for 95% confidence), proportion between 0 and 1, and margin of error as a decimal between 0 and 1.

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use?
A: Common Z-scores are 1.645 (90% confidence), 1.96 (95% confidence), and 2.576 (99% confidence).

Q2: When should I use finite vs infinite population formula?
A: Use finite population formula when your sample represents more than 5% of the total population.

Q3: What if I don't know the proportion (p)?
A: Use 0.5 as it provides the most conservative (largest) sample size estimate.

Q4: How does population size affect sample size?
A: For very large populations, the finite population correction becomes negligible and the formula approaches the infinite population formula.

Q5: What is an acceptable margin of error?
A: Typically 5% (0.05) or 3% (0.03) for most research studies, depending on required precision.