# meaningful difference at a particular point of two cumulative distribution functions

Let's assume we have two distributions: Y and Z.

How can we compare P(x<= 0) in these two distributions?

For example let's say P_Y(x<= 0)=.5 and P_Z(x<= 0)=.65, is there anyway to test if P_Z(x<= 0) is significantly larger than P_Y(x<= 0)?

This amounts to a two-sample binomial test of the two binary variables $$Y\le 0$$ and $$Z\le 0$$.