Trademark Filing Audit Sample Size Estimator

1. Enter the population
Provide the total number of eligible items in the audit population after applying the scope definition.

2. Choose a confidence level
Select 90%, 95%, or 99% depending on the level of statistical confidence required for the planning exercise.

3. Set the margin of error
Enter the desired plus-or-minus precision in percentage points. Smaller margins require larger samples.

4. Estimate the exception rate
Use an expected proportion when you have a reasonable basis. Use 50% as a conservative choice because it produces the largest sample for a given confidence and margin.

5. Review the recommended sample
The result is rounded up to a whole item and cannot exceed the population size.

6. Confirm the sampling method
Draw items randomly or use a more appropriate documented design if the population has meaningful subgroups or risk concentrations.

Initial sample n₀ = z² × p × (1 − p) ÷ e² Finite-population sample n = n₀ ÷ [1 + (n₀ − 1) ÷ N]

Where z is the selected confidence-level critical value, p is the expected exception proportion as a decimal, e is the desired margin of error as a decimal, and N is the population size. The calculator rounds the final result upward to avoid understating the modeled sample requirement.

What the result means

The result is the rounded-up number of items to sample under the selected simple-random-sample assumptions.

Statistical sample size alone does not establish legal or regulatory sufficiency; use the sampling design appropriate to the audit objective and population.

Given
Population: 2,400 items
Confidence level: 95% (z = 1.96)
Margin of error: 5%
Expected exception rate: 50%

Calculation
n₀ = 1.96² × 0.50 × 0.50 ÷ 0.0500² = 384.16
n = 384.16 ÷ [1 + (384.16 − 1) ÷ 2,400] = 331.27
Round up = 332 items

Result
A simple random sample of 332 items meets the selected statistical inputs under this model. The audit design still needs to reflect the purpose, risk profile, and structure of the population.