I'm interested in comparing two independent proportions from two samples. The formula for doing so is available in the Internet (e.g. here). So far, so good.

But my main purpose is not to build a confidence interval. Rather I want to assess how big the second proportion has to be to be significant higher than the first proportion (given an alpha level and both sample sizes).

Suppose I conducted a study and found that 80% of 154 respondents used product X. Suppose further that I will do a second study with the same questions and I'm going for n=200 respondents. How big has this second proportion to be, to be signifcantly higher on a 90% alpha level?

Could anyone provide me with the specific formula which is solved for the second proportion? I know there are online calculators or GPower for exactly such purposes, but unfortunately I have to build up theses formula in Excel and thus have to put them in on my own.

(I originally posted on Stack Overflow, but was told that for statistics I might be better with posting my question here again, so sorry for crossposting!)