Auditing Sample Size Calculator

Sample Size Formula:

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

Sample Size (n):

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1. What is Auditing Sample Size Calculation?

Auditing Sample Size Calculation determines the appropriate number of items to examine in an audit to achieve desired precision and confidence levels. It helps auditors obtain statistically valid results while optimizing audit resources.

2. How Does the Calculator Work?

The calculator uses the sample size formula:

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

Where:

\( n \) — Required sample size
\( Z \) — Z-score (standard normal deviate)
\( E \) — Margin of error (precision)
\( p \) — Expected proportion or prevalence

Explanation: This formula calculates the minimum sample size needed to estimate a population proportion with specified confidence level and margin of error.

3. Importance of Sample Size in Auditing

Details: Proper sample sizing ensures audit conclusions are statistically valid, reduces sampling risk, provides defensible audit evidence, and optimizes audit efficiency by avoiding over-sampling or under-sampling.

4. Using the Calculator

Tips: Enter Z-score based on desired confidence level (e.g., 1.96 for 95% confidence), margin of error as decimal (e.g., 0.05 for ±5%), and expected proportion as decimal (use 0.5 for maximum sample size when uncertain).

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). Choose based on your audit risk tolerance.

Q2: How do I determine the expected proportion?
A: Use historical data, preliminary testing, or conservative estimate of 0.5 (which gives maximum sample size). For compliance testing, use expected error rate.

Q3: What is an appropriate margin of error?
A: Typically 5% (0.05) for most audits, but can range from 1-10% depending on materiality and audit objectives.

Q4: When should I use this formula?
A: For attributes sampling in compliance testing, control testing, and estimating proportions in substantive testing.

Q5: Are there limitations to this approach?
A: Assumes simple random sampling, normal distribution approximation, and may need adjustment for finite populations or stratified sampling.