Choice "C" is correct. The auditor’s allowable risk of assessing control risk too low has an inverse relationship with sample size when planning a sample for a test of controls.
Choice "a" is incorrect. Preliminary judgments about materiality levels might be a consideration in planning an auditor’s sample for a substantive test, but not for a test of controls.
Choice "b" is incorrect. The auditor’s allowable risk of assessing control risk too high is not a factor when planning a sample for a test of controls.
Choice "d" is incorrect. The auditor’s desired level of detection risk might be a consideration in planning an auditor’s sample for a substantive test, but not for a test of controls.