I am interested in calculating the required sample size to achieve some precision using a CI for the mean.
Let's say that I wish to build a 95% CI for the mean, so that the difference between the population mean and the sample mean won't be larger than 2 units (with 95% confidence), and I assume a S.D of 5 units. To do so, I play a bit with the formula, extract N, and being an exact calculation, I get what I want. In the case of t (rather than z), the computer will do it and give me N = 27. Now I tried to do it with SAS, and I found this source.
Apparently, SAS adds another dimension to the calculation, which is an equivalent to the power of hypothesis testing. I don't understand why is it necessary in the first place. Using the CI formula, if N = 27 give a precision of 2, isn't it enough ? For 80% "power" I get N = 32, and for 90% "power" I get N = 35, while all along I find N = 27 to be sufficient.
Can you please help me understand when should I use the simple direct method coming from the formula and when should I use this approach by SAS (and probably others)?