Answer:
Step-by-step explanation:
[tex]p_1 = \frac{r_1}{n_1} \\p_2= \frac{r_2}{n_2} \\[/tex]
Pooled proportion
[tex]p = \frac{r_1+r_2}{n_1+n_2}[/tex]
The hypothesis null would be
[tex]H_0: p_1-p_2 =0[/tex]
Alternate can be either not equal to or < or > according to need
Std error for difference of proportions
[tex]=\sqrt{p(1-p)(\frac{1}{n_1} +\frac{1}{n_2}}[/tex]
Hence test statistic = p difference/std error
= [tex]\frac{\frac{r_1}{n_1}- \frac{r_2}{n_2}}{\sqrt{p(1-p)(\frac{1}{n_1} +\frac{1}{n_2}}}[/tex]
where p is given as above as combined proportion.
