43. Bullies in middle school A University of Illinois study on aggressive behavior surveyed a random sample of 558 middle school students. When asked to describe their behavior 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.12 Is this evidence that more than three-quarters of middle school students 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.

H0 : p = 0.75 Ha : p^ > 0.797 where p = the true mean proportion of middle school students who engaged in bullying.

• A random sample of 558 middle school students was surveyed.

• 558(0.797) = 444.73 is at least 10.

z =

0.75 − 0.797

"0.797(0.203)

445

= −2.46; P-value = 2(0.0069) = 0.0138 The probability that the null hypothesis is true is only 0.0138, so we reject H0. This proves that more than three-quarters of the school engaged in bullying behavior.