Final answer:
An increase in tolerable misstatement leads to a decrease in sample size, while an increase in assessed level of control risk results in an increase in sample size for a substantive test of details. This is because tolerable misstatement reflects the amount of risk auditors are willing to accept, and assessed control risk indicates the trust in the client's internal controls.
Step-by-step explanation:
How increases in tolerable misstatement and assessed level of control risk affect the sample size in a substantive test of details is important in audit procedures. The correct answer for how these factors affect sample size is option (b): Increase in Tolerable Misstatement equals Decrease sample size. Increase in Assessed Level of Control Risk equals Increase sample size. This is because a higher tolerable misstatement indicates a willingness to accept a higher level of error, thus reducing the need to examine as many items. On the other hand, a higher assessed level of control risk implies that the auditor has less confidence in the effectiveness of the client's control environments, necessitating a larger sample size to capture the true nature of the transactions or account balances.
When it comes to altering the sample size, understanding its relationship with error bounds and confidence levels is crucial. A decrease in error bound would require an increase in the minimum sample size if we wish to maintain the same level of confidence, because smaller sample sizes result in increased variability. To capture the true population mean with a high level of confidence and a low error bound, a larger sample size is necessary. Conversely, if one were to increase the error bound, a smaller sample size would be sufficient.