Audit Sample Size Calculator

Audit Sample Size Formula:

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

Z-Score (Z):

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Population Size (N):

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Proportion (p):

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Margin of Error (E):

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Sample Size (n):

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1. What is the Audit Sample Size Calculator?

The Audit Sample Size Calculator determines the appropriate sample size for statistical sampling in audit procedures. It uses the standard sample size formula to ensure representative and reliable results for audit testing.

2. How Does the Calculator Work?

The calculator uses the statistical sampling formula:

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

Where:

\( n \) — Required sample size
\( Z \) — Z-score (confidence level)
\( N \) — Population size
\( p \) — Estimated proportion
\( E \) — Margin of error

Explanation: This formula calculates the minimum sample size needed to achieve a desired level of precision and confidence in audit sampling.

3. Importance of Sample Size Calculation

Details: Proper sample size calculation ensures audit efficiency, statistical reliability, and appropriate coverage of the population being tested. It helps auditors draw valid conclusions about the entire population based on sample results.

4. Using the Calculator

Tips: Enter Z-score (typically 1.96 for 95% confidence), population size, estimated proportion (0.5 for maximum variability), and margin of error (typically 0.05 for 5% margin).

5. Frequently Asked Questions (FAQ)

Q1: What is the recommended Z-score for audit sampling?
A: For 95% confidence level, use Z = 1.96; for 99% confidence, use Z = 2.576.

Q2: Why use p = 0.5 as default?
A: p = 0.5 provides the most conservative estimate and maximum sample size, ensuring adequate coverage when the true proportion is unknown.

Q3: What is an acceptable margin of error for audits?
A: Typically 5% (0.05) is used, but this can vary based on audit risk tolerance and materiality considerations.

Q4: When should this formula not be used?
A: For very small populations (N < 30) or when sampling without replacement assumptions are violated.

Q5: How does population size affect sample size?
A: For large populations, sample size becomes relatively stable, while for small populations, sample size represents a larger proportion of the total.