- Use this test when in both samples there are $5$ or more successes (i.e., $n_1\hat{p}_1\geq 5$ and $n_2 \hat{p}_2\geq 5$) and $5$ or more failures (i.e., $n_1(1-\hat{p}_1)\geq 5$ and $n_2(1-\hat{p}_2)\geq 5$).
- When the above guidelines for this test are not met, you may use a non-parametric alternative: Bootstrap Test for the Difference of Two Population Proportions.
| Number of Successes | Sample Size $n$ | |
| Sample 1: | $k_1=$ | $n_1=$ |
| Sample 2: | $k_2=$ | $n_2=$ |
| Null Hypothesis: | $H_0: p_1=p_2$ | |
| Alternative Hypothesis: | $H_a: p_1$ $p_2$ | |
| Significance Level: | $\alpha=$ |
| Sample Size: | $n_1=$ | $n_2=$ |
| Sample Proportions: | $\hat{p}_1=$ | $\hat{p}_2=$ |
| Difference Estimate: | $\hat{p}_1-\hat{p}_2=$ | |
| Pooled Sample Proportion: | $\hat{p}_{pool}=$ | |
| Standard Error: | $\mbox{SE}_{\hat{p}_{pool}}=$ | |
| Critical $z$ Value: | $z^{*}=$ | |
| $z$ Statistic: | $z=$ | |
| $p\mbox{-value}$: | $p\mbox{-value}=$ |