My experience with statistics is very limited although I understand probability theory quite well. My friend, an accountant, asked a question. He does attribute sampling. I understand most of it intuitively and the math was what I expected it to look like when I got curious and started reading. In determining the sample size necessary they set a confidence level based on the risk they are willing to take and a tolerable deviation which is the maximum acceptable percentage of the population with the attribute. The weird thing is that, in addition, they use an "expected deviation" which appears to be a guess at the result. They use this guess, combined with the other two factors to determine the sample size. According to him, they just set the expected deviation according to how much work they want to do. If the expected deviation is low then the sample size is smaller and they do less work. So, my question is, is there a theoretical basis for using this estimated deviation in the determination of necessary sample size? If so, is there a reference that would explain this to me. I'm sure that setting it on the basis of how motivated one feels today is not necessarily valid.