# sample size of infinite population and alternative comparisson

I need to compare two alternative methods of manufacturing a product, say A and B. I wanted first to dermine the sample size of the measurings, and found this post in a sister site. There, it says that the number of samples is a function of the Z-value for a desired confidence, the standard deviation and the expected difference between alternatives. At first, it seemed to solve my problem, but then it sparked more questions than I had before. That's why I come here for help (I think the subject belongs more to the specialized CV site that to the general Mathematics, that's why I came with it here instead of there):

1. What should I use for standard deviation? The post contains σ which is normally used to designate the population's standard deviation. Obviously I don't have it, so I assume I should use the sample's instead (see here, for example). The problem is, those two are different for small sample sizes, so there comes a "recursive" what sample size should I take?
2. There's only one standard deviation, and I want to compare two alternatives. Does it mean that I should determine a sample size for each alternative, depending on its sd? or I should define the sample size as the max of the two estimated numbers.
3. Is there any comparisson (preferably numerical) to determine that indeed there's one alternative that is better than the other? If so, what test should I run?

Thanks,

• If knowing $\sigma$ would make using a Z suitable, replacing it with a $t$ and using sample standard deviation $s_{n-1}$ should usually be adequate for the case where you don't know $\sigma$. – Glen_b -Reinstate Monica Aug 1 '15 at 2:16