Question

A University of Illinois study on aggressive behavior surveyed a random sample of 558 middle school students. When asked to describe their behaviors in the last 30 days, 445 students said their behavior included physical aggression, social ridicule, teasing, name-calling, and issuing threats. This behavior was not defined as bullying in the questionnaire. $^{14}$ Is this evidence that more than three-quarters of the students at that middle school engage in bullying behavior? To find out, Maurice decides to perform a significance test. Unfortunately, he made a few errors along the way. Your job is to spot the mistakes and correct them. $$\begin{aligned}&H_{0}: p=0.75\\&H_{a}: p \geqslant 0.797\end{aligned}$$ where $p=$ the true mean proportion of middle school students who engaged in bullying. $\bullet$ A random sample of 558 middle school students was surveyed. $\bullet 558(0.797)=444.73$ is at least $10 .$ $$z=\frac{0.75-0.797}{\sqrt{\frac{0.797(0.203)}{445}}}=-2.46_{i} P_{\text{value}}=2(0.0069)=0.0138$$ The probability that the null hypothesis is true is only $0.0138,$ so we reject H$_{o}$. This proves that more than three-quarters of the school engage in bullying behavior.

          A University of Illinois study on aggressive behavior surveyed a random sample of 558 middle school students. When asked to describe their behaviors in the last 30 days, 445 students said their behavior included physical aggression, social ridicule, teasing, name-calling, and issuing threats. This behavior was not defined as bullying in the questionnaire. $^{14}$ Is this evidence that more than three-quarters of the students at that middle school engage in bullying behavior? To find out, Maurice decides to perform a significance test. Unfortunately, he made a few errors along the way. Your job is to spot the mistakes and correct them.
$$\begin{aligned}&H_{0}: p=0.75\\&H_{a}: p \geqslant 0.797\end{aligned}$$
where $p=$ the true mean proportion of middle school students who engaged in bullying.
$\bullet$ A random sample of 558 middle school students was surveyed.
$\bullet 558(0.797)=444.73$ is at least $10 .$
$$z=\frac{0.75-0.797}{\sqrt{\frac{0.797(0.203)}{445}}}=-2.46_{i} P_{\text{value}}=2(0.0069)=0.0138$$
The probability that the null hypothesis is true is only $0.0138,$ so we reject H$_{o}$. This proves that more than three-quarters of the school engage in bullying behavior.

Added by David B.

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