Independent random samples, each containing $600$ observations, were selected from two binomial populations. The samples from populations 1 and 2 produced $386$ and $192$ successes, respectively.
(a) $\ $ Test $H_0: (p_1 - p_2) = 0$ against $H_a: (p_1 - p_2) \ne 0$. Use $\alpha = 0.08$

test statistic $=$

rejection region $|z| >$

The final conclustion is

A. There is not sufficient evidence to reject the null hypothesis that $(p_1 - p_2) = 0$.
B. We can reject the null hypothesis that $(p_1 - p_2) = 0$ and accept that $(p_1 - p_2) \ne 0$.

(b) $\ $ Test $H_0: (p_1 - p_2) = 0$ against $H_a: (p_1 - p_2) > 0$. Use $\alpha = 0.1$

test statistic $=$

rejection region $z >$

The final conclustion is

A. There is not sufficient evidence to reject the null hypothesis that $(p_1 - p_2) = 0$.
B. We can reject the null hypothesis that $(p_1 - p_2) = 0$ and accept that $(p_1 - p_2) > 0$.