Statistics for Business: Decision Making and Analysis, 3rd Edition

... for rejecting H₀ depends on the level α and the sample sizes in the two groups, n₁ and n₂.

two-sample z-test for proportions.

Test of H₀: p₁ − p₂ ≤ D₀ using the two-sample z-statistic.

Population parameters	p1, p2
Null hypothesis	H0: p1 − p2 ≤ D0
Alternative hypothesis	Ha: p1 − p2 > D0
Sample statistic	${\widehat{p}}_1-{\widehat{p}}_2$
Estimated standard error	$\text{se}\left({\widehat{p}}_1-{\widehat{p}}_2\right)=\sqrt{\frac{{\widehat{p}}_1\left(1-{\widehat{p}}_1\right)}{n_1}+\frac{{\widehat{p}}_2\left(1-{\widehat{p}}_2\right)}{n_2}}$
z-statistic	$z=\left({\widehat{p}}_1-{\widehat{p}}_2-D_0\right)\text{se}\left({\widehat{p}}_1-{\widehat{p}}_2\right)$
Reject H0 if	p-value < α or z > za

The following checklist insures that the z-test is reliable. The checklist for two-sample comparisons is longer than those for the one-sample test. The first two conditions in the checklist are the most important and require background knowledge of the situation and data. You cannot verify these ...