Final answer:
The statement that 'If materiality decreases, sample size will need to increase' best describes the relationship between sample size and audit elements. Larger samples lead to more reliable statistics and decrease sampling variability, thereby enhancing the reliability of the audit findings.
Step-by-step explanation:
The relationship between sample size and other elements of auditing is essential to understand for accurate results. The correct statement that best describes this relationship is: If materiality decreases, sample size will need to increase. This is because when the tolerable level of misstatement (materiality) is lower, auditors need to have greater assurance that the financial statements are free of material misstatement, which often involves increasing the sample size to get a more precise representation of the population. Furthermore, the desire for a higher level of assurance demands larger sample sizes, not smaller ones, to decrease the risk of an incorrect conclusion. Conversely, if materiality increases, implying that larger misstatements are acceptable, the sample size can be smaller because less assurance is required that the financial statements are accurate down to the smaller details. Sampling variability also plays a role in determining the right sample size. Smaller samples can yield results that differ significantly from the population average, while larger samples tend to produce more reliable statistics that are reflective of the population. Therefore, larger sample sizes can enhance the reliability of audit findings and decrease sampling error.