easyMultiple ChoiceObjective-mapped
Factors Increasing Sample Size in Statistical Sampling
An IS auditor is using statistical sampling to test a population of 10,000 transactions. The desired confidence level is 95%, and the tolerable error rate is 5%. Which of the following factors would MOST likely increase the required sample size?
Quick Answer
An increase in the expected error rate to 6% is the correct choice because it directly increases the required sample size in statistical sampling. This occurs because the sample size formula is proportional to the product of the expected error rate and its complement (p × (1-p)), and as the expected error rate moves toward 50%, this product—and thus the variance—grows, demanding a larger sample to maintain precision at a fixed confidence level. On the CISA exam, this principle tests your understanding of how changes in the expected error rate, not the tolerable error rate or population size, drive sample size adjustments; a common trap is assuming a lower tolerable error rate always increases sample size, but here the key is the shift in expected error rate. Remember the memory tip: “p times (1-p) peaks at 50%”—so when the expected error rate climbs toward the middle, your sample size must climb too.
⚠ Common exam trap
The trap here is that candidates mistakenly think increasing population size always increases sample size, but in statistical sampling for large populations, the population size has a diminishing effect and is not the primary driver of sample size.
Answer choices
Why each option matters
Answer the question above first, then reveal the full breakdown to understand why each option is right or wrong.
Correct answer & explanation
✓
An increase in the expected error rate to 6%
An increase in the expected error rate increases the required sample size because the sample size formula includes the term p × (1-p), where p is the expected error rate. As p increases from 5% to 6%, this product increases, raising the variance and thus the sample size. While a decrease in tolerable error rate also increases sample size, the question asks for the factor that most likely increases sample size in the context of audit sampling. An increase in expected error rate directly signals higher risk, making it the primary driver for increasing sample size. Therefore, option A is correct.
Answer analysis
Option-by-option breakdown
For each option: why learners choose it and why it is or isn't the right answer here.
- ✓
An increase in the expected error rate to 6%
Why this is correct
Increasing the expected error rate to 6% increases the product p×(1-p) in the sample size formula, thus increasing sample size. This is the correct answer.
- ✗
A decrease in the tolerable error rate to 3%
Why it's wrong here
Decreasing the tolerable error rate to 3% actually reduces the required sample size because the allowable error is smaller, meaning you need less evidence to detect that small error. Therefore, this does not increase sample size.
- ✗
A decrease in the confidence level to 90%
Why it's wrong here
Decreasing the confidence level reduces the z-value, which decreases sample size.
- ✗
An increase in the population size to 15,000
Why it's wrong here
Increasing population size has a negligible effect on sample size for large populations.
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Variation 1. Which of the following is the most important factor to consider when determining sample size for a compliance test?
easy- ✓ A.Tolerable error rate
- B.Expected error rate
- C.Population size
- D.Sampling method
Why A: In compliance testing (attribute sampling), the tolerable error rate is the maximum deviation rate from a control that the auditor is willing to accept without concluding the control is ineffective. It directly determines the required sample size because a lower tolerable error rate demands a larger sample to achieve sufficient precision, while a higher rate allows a smaller sample. This factor is more critical than others because it sets the boundary for the auditor's risk assessment.
JA
Written by Johnson Ajibi, MSc IT Security
Senior Network & Security Engineer · founder of Courseiva
This CISA practice question is part of Courseiva's free ISACA certification practice question bank. Courseiva provides original exam-style practice questions with explanations, topic-based practice, mock exams, readiness tracking, and study analytics to help learners prepare for the CISA exam.