Final answer:
There is a direct relationship between assurance and sample size in audit sampling. Larger sample sizes provide more reliable estimates and reduce sampling variability, making the sample more representative of the population.
Step-by-step explanation:
With respect to audit sampling, the correct statement is that there is a direct relationship between assurance and sample size. This means the more assurance the auditor requires, the larger the sample size they will need to select. Various factors influence audit sampling, like the desired level of assurance, the risk of material misstatement, and the allowable sampling error. Selecting a sample that represents the population is critical, which is best achieved through random sampling.
When selecting a sample size, auditors follow the statistical theory that larger sample sizes generally lead to more reliable conclusions about the population. This is because larger samples reduce sampling variability and provide more accurate and closer estimates to true population characteristics. However, the auditor must always navigate the practical limitations, such as cost and time constraints, when determining the sample size.
Furthermore, when paired or matched samples are used in a hypothesis test, it typically involves comparisons between two sets of measurements from the same set of items or individuals, which accounts for the dependence between measurements.
In summary, the importance of an appropriate sample size cannot be overstated in audit sampling. Random sampling is effective because it provides each member of the population with an equal chance of being included, thereby creating an unbiased sample that best represents the entire population.