In a survey of 240 males ages 20 to \( 24,35 \% \) were neither in school nor working. In a survey of 220 females ages 20 to \( 24,41 \% \) were neither in school nor working. These samples are random and independent. At \( \alpha=0.05 \), can you support the claim that the proportion of males ages 20 to 24 who were neither in school nor working is less than the proportion of females ages 20 to 24 who were neither in school nor working? Complete parts (a) through (e) below.
(a) Identify the claim and state \( \mathrm{H}_{0} \) and \( \mathrm{H}_{\mathrm{a}} \).
The claim is "the proportion of males ages 20 to 24 who were neither in school nor working is less than the proportion of females ages 20 to 24 who were neither in school nor working."
Let \( p_{1} \) and \( p_{2} \) be the two population proportions for males and females, respectively. State \( H_{0} \) and \( H_{a} \).
Choose the correct answer below.
A. \( H_{0}: p_{1}=p_{2} \)
B. \( H_{0}: p_{1} \leq p_{2} \)
\[
\begin{array}{l}
H_{0}: p_{1}<p_{2} \\
H_{a}: p_{1}>p_{2}
\end{array}
\]
\[
H_{a}: p_{1} \neq p_{2}
\]
E. \( H_{0}: p_{1}<p_{2} \)
\[
\begin{array}{l}
H_{0}: p_{1} \neq p_{2} \\
H_{a}: p_{1}=p_{2}
\end{array}
\]
\[
\begin{array}{l}
H_{0}: p_{1}<p_{2} \\
H_{a}: p_{1} \geq p_{2}
\end{array}
\]
C. \( H_{0}: p_{1} \geq p_{2} \) \( H_{a}: p_{1}<p_{2} \)
(b) Find the critical value(s) and identify the rejection region(s).
The critical value(s) is(are) \( \square \)
\( \square \)
(Use a comma to separate answers as needed. Round to two decimal places as needed.)