Final answer:
The size of a random sample is primarily influenced by the level of risk that an organization has accepted, particularly in the context of detecting fraud, rather than other factors like the population size or accounting practices.
Step-by-step explanation:
The size of a random sample is most dependent on C. the level of risk that the organization has accepted. When deciding on the size of a sample, it is essential to consider the acceptable level of risk which includes the risk of not detecting fraud or error in the population. The size of the population, the basis of accounting used, and the size of the internal audit function, while relevant to broader processes and controls, do not have a direct influence on the size determination of the sample used for testing in audits and research.
An appropriately sized sample minimizes the risk of an assertion being incorrect while considering both cost-efficiency and effectiveness. Larger samples reduce sampling variability, thereby providing a better representation of the population and more reliable results. The right sample size strengthens the study's validity and establishes a solid foundation for generalizations about the larger population.