"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 depression in a group of bully-victims and a group of bystanders using an 18-item, 5-point depression scale. Assume scores on the depression scale are normally distributed and that the variances of the depression scores are the same among bully-victims and bystanders. The group of 39 bully-victims scored an average of 51.6 with a sample standard deviation of 9 on the depression scale. The group of 31 bystanders scored an average of 45.2 with a sample standard deviation of 12 on the same scale. You do not have any presupposed assumptions about whether bully-victims or bystanders will be more depressed, so you formulate the null and alternative hypotheses as: Ho: Hbully-victims - Pbystanders H1: Pbully-victims - Pbystanders You conduct an independent-measures t test. Given your null and alternative hypotheses, this is a test. To use the Distributions tool to find the rejection region, you first need to set the degrees of freedom. The degrees of freedom is t Distribution Degrees of Freedom = 78 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 AAN t The critical t-scores that form the boundaries of the rejection region for a = 0.05 are ± In order to calculate the t statistic, you first need to calculate the standard error under the assumption that the null 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(M1 – M2) = The t statistic is The t statistic in the rejection region. Therefore, the null hypothesis is You conclude that bully- victims have a different mean depression score than bystanders. Thus, it can be said that these two means are different from one another.