Stats.Blue

# Hypothesis Test for Two Population Proportions

• 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 $n_2(1-\hat{p}_2)\geq 5$).
 Sample Sizes: $n_1=$ $n_2=$ Sample Proportions: $\hat{p}_1=$ $\hat{p}_2=$ Null Hypothesis: $H_0: p_1=p_2$ Alternative Hypothesis: $H_a: p_1$ $\neq$ $<$ $>$ $p_2$ Significance Level: $\alpha=$ 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005

 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: $z^{*}=$ % Confidence Interval: $z$ Statistic: $z=$ $p$ value: $p=$