*z*-Test

**Details:** The null hypothesis is that *x*_{1}-*x*_{2} is
normally distributed with mean 0 and variance σ_{1}^{2}+σ_{2}^{2}.
Typically *x*_{1}-*x*_{2} is not zero, and we find the probability
that it could be that or more divergent, e.g., if |*z*|=2 we would calculate the area *P* shaded below:

In general *P* can be plotted as a function of |*z*|

"critical" (i.e., commonly used) values

|z| P
0.674 0.5
1 0.317
1.645 0.1
1.960 0.05
2 0.0455
2.576 0.01
2.807 0.005
3 0.00270
3.291 0.001
3.481 0.0005
3.891 0.0001
4 0.0000633