Calculation Of Sample Size Formula

Finite Population Sample Size Formula:

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

Population Size (N):

individuals

Z-Score:

Proportion (p):

decimal

Margin of Error (E):

decimal

Required 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 for surveys and studies when the total population size is known. It provides a more precise estimate than the infinite population formula when sampling from smaller populations.

2. How Does The Calculator Work?

The calculator uses the finite population sample size formula:

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

Where:

\( n \) — Required sample size
\( N \) — Total population size
\( Z \) — Z-score (confidence level)
\( p \) — Estimated proportion (0.5 for maximum variability)
\( E \) — Margin of error

Explanation: This formula adjusts for finite population correction, providing more accurate sample sizes when the population is not extremely large.

3. Importance Of Sample Size Calculation

Details: Proper sample size calculation ensures study validity, adequate statistical power, and reliable results while optimizing resource allocation and minimizing sampling error.

4. Using The Calculator

Tips: Enter population size, select confidence level (Z-score), provide estimated proportion (use 0.5 for conservative estimate), and specify desired margin of error. All values must be valid and within acceptable ranges.

5. Frequently Asked Questions (FAQ)

Q1: When Should I Use The Finite Population Formula?
A: Use when your population size is known and relatively small (typically under 100,000). For very large populations, the infinite population formula may suffice.

Q2: What Z-Score Should I Choose?
A: 1.96 for 95% confidence (most common), 1.645 for 90% confidence, or 2.576 for 99% confidence depending on your required confidence level.

Q3: Why Use p = 0.5 As Default?
A: p = 0.5 provides the maximum sample size (most conservative estimate) since p × (1-p) reaches its maximum value at 0.5.

Q4: What Is A Reasonable Margin Of Error?
A: Typically 5% (0.05) for most surveys, but can range from 1% to 10% depending on precision requirements and available resources.

Q5: How Does Population Size Affect Sample Size?
A: As population increases, the required sample size increases but at a decreasing rate. Very large populations require only marginally larger samples.