Final answer:
The auditor would need to increase the level of control testing when the risk of material misstatement is high or when they have less confidence in the organization's internal controls. For the survey scenarios, a larger or better-chosen sample is required to maintain confidence levels while keeping the error bound constant. Reducing the sample size would decrease confidence levels.
Step-by-step explanation:
To answer the question regarding which conditions would require the auditor to increase the level of control testing for a particular control, it's important to understand the concept of audit risk. If an auditor finds that there is a high risk of material misstatement or if they have less confidence in the effectiveness of an organization's internal controls, they may decide to increase the extent of control testing. This could occur in instances where there's a history of errors, instances of fraud, significant changes in personnel or systems, or simply when the auditor is seeking higher assurance.
In the scenarios you've provided (e and f), increasing the level of confidence in the test results while keeping the error bound the same generally requires increasing the sample size or improving the selection methodology of the sample. In the case where the firm reduces the sample size to 49, on the other hand, the level of confidence in the survey results would decrease because the smaller sample size is less representative of the population, thereby increasing the sampling risk.