**Re: What are these formulas and what is their purpose? n=(sigma^2)(Z_alpha/h^2); two **

They're both sample size calculations. The first is when you know the population standard deviation (or are willing to assume a value for it), know what confidence level you want, and know how wide you want the interval to be. They call the width of the interval w. Sometimes people instead characterize this using the half-width (half the width of the interval) and they call that h.

The second does look to be a sample size calculation for a two sample z-test.