A research study was conducted about gender differences in sexting, the sending of sexually explicit messages or images by cell phone. A researcher believes that the proportion of girls sexting is less than the proportion of boys sexting and decides to collect data in the spring of 2010 among a random sample of middle and high school students in a large school district in the southem United States. The researcher finds 156 out of 2,169 girls are sexting and 183 out of 2,231 boys are sexting. Is there enough evidence to support the researcher's belief that the proportion of girls sexting is less than the proportion of boys sexting? Test at the 0.1 level of significance.
Preliminary:
a. Is it safe to assume that:
\( n_{\text {girls }} \leq 5 \% \) of all girls in middle and high school students in a large school district in the southern United States and
\( n_{\text {boys }} \leq 5 \% \) of all boys in middle and high school students in a large school district in the southern United States?
Yes
No
b. Verify \( n \hat{p}(1-\hat{p}) \geq 10 \). Round your answer to one decimal place.
\[
\begin{array}{l}
n_{\text {giris }} \hat{p}(1-\widehat{p})=\square \\
n_{\text {bovi }} \hat{p}(1-\hat{p})=\square
\end{array}
\]
Test the claim:
a. Determine the null and alternative hypotheses.
\[
\begin{array}{l}
H_{0}: p_{\text {girls }} ? \vee \text { Pboys } \\
H_{a}: p_{\text {girk }} ? \vee \text { Pboys }
\end{array}
\]
b. The hypothesis test is Select an answer \( v \)
c. Determine the test statistic. Round to two decimal places.
\[
z=\square
\]
d. Find the \( p \)-value. Round to four decimal places.
\[
p \text {-value }=
\]
\( \square \)
e. Make a decision.
Reject the null hypothesis.
Fail to reject the null hypothesis.
f. Write the conclusion.
There is not sufficient evidence to support the claim that the proportion of girls sexting is less
