"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 bullies and a group of bully-victims 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 bullies and bully-victims. the group of 39 bullies scored an average of 51.6 with a sample standard deviation of 9 on the depression scale. the group of 31 bully-victims 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 bullies or bully-victims will be more depressed, so you formulate the null and alternative hypotheses as: h 0 : μ bullies – μ bully-victims = 0 h 1 : μ bullies – μ bully-victims ≠ 0 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 .