Final answer:
An auditor will reduce reliance on a control when the combined sample deviation rate and allowance for sampling risk exceed the tolerable deviation rate, indicating a higher than acceptable error rate in the internal control system.
Step-by-step explanation:
An auditor who uses statistical sampling for attributes in testing internal controls is most likely to reduce the planned reliance on a prescribed control when the sample deviation rate plus the allowance for sampling risk exceeds the tolerable deviation rate. This is because the sum of the sample deviation rate and the allowance for sampling risk represents the upper limit of the error rate the auditor is willing to accept. If this sum exceeds the tolerable deviation rate, then the actual deviation rate in the internal control may be too high, thus reducing the auditor's confidence in the control and leading to decreased reliance on it.
As for statistical concepts, to lower the sampling error, one could increase the sample size, ensuring a more accurate representation of the population. The ±3 percent sampling error mentioned indicates a confidence interval which suggests that there is a 95% chance that the true population parameter lies within 3 percentage points above or below the observed sample statistic.
To ensure the validity of the normal test for statistical inference, assumptions such as simple random sampling, known standard deviation, and a sufficiently large sample size or normal distribution of the population are necessary. Experimental controls are aspects of a study designed to increase the validity of the results, such as controlling variables to focus on the effects of one independent variable (experimental controls).