Zapis hipotez do testowania różnicy dwóch proporcji

Researchers want to study the effectiveness of a new medication to treat depression. In a randomized experiment, $71$‍ out of $200$‍ people taking the medication report symptoms of depression. Of the people receiving a placebo, $92$‍ out of $200$‍ report symptoms of depression. The researchers want to use these results to test if the medication is working any differently than the placebo.

Let $p_1$‍ be the true proportion of individuals like the ones in this study who take the new medication and report symptoms of depression, and $p_2$‍ be the true proportion of individuals like the ones in this study who take a placebo and report symptoms of depression.