Determining an appropriate sample size is crucial in audit sampling to ensure results are statistically reliable and cost-effective. Key factors impacting sample size include population size, confidence level, variability (standard deviation), tolerable misstatement, and expected misstatement. One formula that explicitly incorporates population size is:

Sample Size=( (Population Size × Confidence Coefficient × Standard Deviation)/ (Tolerable Misstatement−Estimated Misstatement) )2

Where:

• $N$ = population size

• $Z$ = confidence coefficient (Z-score)

• $\sigma$ = estimated standard deviation

• $TM$ = tolerable misstatement

• $EM$ = expected misstatement

For example, an auditor testing 10,000 accounts receivable uses a 90% confidence level ($Z=1.64$) with an estimated standard deviation of $20. The tolerable misstatement is $40,000, and the expected misstatement is $15,000. Applying the formula:

This means the auditor should sample approximately 172 accounts. This larger sample size reflects the substantial population and relatively narrow margin between tolerable and expected misstatement, ensuring the audit provides sufficient assurance.

In summary, incorporating population size directly in the sample size formula can lead to more conservative sampling and better risk mitigation, though auditors must balance practicality and efficiency in final sample decisions.