Determine $($a$)$ the ${}^2$ test statistic, $($b$)$ the degrees of freedom, $($c$)$ the P$-$value, and $($d$)$ test the hypothesis at the $=0\mathrm{.}05$ level of significance.

$\backslash$table$[[$Outcome$,$A$,$B$,$C$,$D$],[$Observed$,48,52,47,53],[$Expected$,50,50,50,50]]$

$H_0$:$p_A=p_B=p_C=p_D=\frac{1}{4}$

$H_1$ : At least one of the proportions is different from the others.

$($a$)$ The test statistic is

$($Round to two decimal places as needed.$)$

$($b$)$ There are degrees of freedom.

$($Type a whole number.$)$

$($c$)$ The P$-$value is

$($Round to three decimal places as needed.$)$

$($d$)$ What is the conclusion of the test at the $=0\mathrm{.}05$ level of significance?

the null hypothesis, because the P$-$value is than There sufficient evidence that the random variable does not follow the snecified distribution.