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 m 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 victims 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 victims and bully-victims. The group of 23 victims scored an average of 40.1 with a sample standard deviation of 10 on the depression scale. The group of 28 bully-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 victims or bully-victims will be more depressed, so you formulate the null and alternative hypotheses as:.
H0:μvictims - μ bully victims = 0
H1:μvictims - 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 critical region, you first need to set the degrees of freedom.