You wish to test the following claim $(H_a)$ at a significance level of $=0\mathrm{.}01.$

$H_o$:$p_1=p_2$

$H_a$:$p_1{p}_2$

The $1$st population's sample has $83$ successes and a sample size $=414.$

The $2$nd population's sample has $47$ successes and a sample size $=401.$ What is the test statistic $($z$-$score$)$ for this sample? $($Round to $3$ decimal places.$)$

test statistic $=$

What is the $p-$value for this sample? $($Round to $3$ decimal places.$)$

$p-$value $=$

The $p-$value is$...$

less than $($or equal to$)$

greater than $$

This test statistic leads to a decision to$...$

reject the null

fail to reject the null

accept the null

As such, the final conclusion is that...

The sample data support the alternate hypothesis claim that p$1$ is not equal to p$2.$

There is not sufficient sample evidence to support the alternate hypothesis claim that p$1$ is not equal to $p2.$