Why would this solution be an upper-tailed rather than a lower-tailed?

Question

Confused I thought if the alternative hypothesis was greater than the null hypothesis then we would do a upper-tailed? Thank you

Answer 1

If your test-statistic is of the form $$Z^{*}=\frac{\hat{p}_1-\hat{p}_2 }{\sqrt{p^{*}(1-p^{*})(\frac{1}{n_1}+\frac{1}{n_2})}}$$ where, $p^{*}=\frac{x_1+x_2}{n_1+n_2}$

Now if $\hat{p}_1$ is significantly greater than $\hat{p}_2$, your test statistic falls in the upper tail region of the Normal distribution.

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