Conduct a test at the $=0\mathrm{.}10$ level of significance by determining $($a$)$ the null and alternative hypotheses, $($b$)$ the test statistic, $($c$)$ the critical value, and $($d$)$ the $P-$value. Assume the samples were obtained independently from a large population using simple random sampling.

Test whether $p_1>p_2.$ The sample data are $x_1=118,n_1=254,x_2=135,$ and $n_2=319.$

$($a$)$ Choose the correct answer.

A$.H_0$:$p_1=p_2$ versus $H_1$:$p_1>p_2$

B$.H_0$:$p_1=0$ versus $H_1$:$p_{1}0$

C$.H_0$:$p_1=p_2$ versus $H_0$:$p_1=p_2{H}_1$:$p_1{p}_2{H}_1$:$p_1$

$D.H_0$:$p_1=p_2$ versus $H_1$:$p_1{p}_2$