(Solved): 5. The t test for two independent samples - Two-tailed example "Bullying," according to noted exper ...

5. The $t$ test for two independent samples - Two-tailed example "Bullying," according to noted expert Dan Olweus, "poisons the educational environment and affects the learning of every child," Bullying and victimization are evident as early as preschool, with the problem peaking in middle school. suppose you are interested in the emotional well-being of not only the victims but also bystanders, bullies, and those who bully but who are also victims (bully-victims). You decide to measure anxiety in a group of bullies and a group of victims using an 18 -item, 5-point anxiety scale. Assume scores on the anxiety scale are normally distributed and that the variances of the anxiety scores are the same among bullies and victims. The group of 23 bullies scored an average of 40.1 with a sample standard deviation of 10 on the anxiety scale. The group of 28 victims scored an average of 46.8 with a sample standard deviation of 11 on the same scale. You do not have any presupposed assumptions about whether bullies or victims will be more anxious, so you formulate the null and alternative hypotheses as: $H_0:H_{\text{trillet }}?$ Hvitim. $=0$ $H_1:H_{\text{billes }}?H_{\text{vitim }}+0$ You conduct an independent-measures $t$ test. Given your null and alternative hypetheses, this is a test. To use the Distributions tool to find the rejection region, you first need to sat the degrees of freedom. The degrees of freedom is Gegrent of Fitedom $=\mathrm{sig}$ The critical t-scores that form the boundaries of the rejection region for $a=0.05$ are \pm In order to calculate the t statistic, you first need to calculate the standard error under the assumption that the nult hypothesis is true. In order to calculate the standard error, you first need to calculate the pooled variance. The pooled variance is s? $=$ . The standard error is $s$ $\text{ (Mi-Mz }=$ The t statistic is The $t$ statistic in the rejection region. Therefore, the null hypothesis is . You conclude that buliles have a different mean anxiety score than victims. Thus, it can be said that these two means are different from ane another.