Computational Details

Because the null hypothesis assumes equal proportions, $p_1=p_2$ , we compute a pooled estimate $\hat{p}$ as follows:

$$\hat{p}\;=\;\frac{n_1\cdot\hat{p}_1+n_2\cdot\hat{p}_2}{n_1+n_2}$$

(This value appears in cell B14)

The $z$ -statistic for testing equality of the population proportions $p_1$ and $p_2$ is:

$$Z\;=\;\frac{\hat{p}_1-\hat{p}_2}{\sqrt{\hat{p}(1-\hat{p}}\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$$

(This value appears in cell B17)