5. The t test for two independent samples Two-tailed example Aa Aa \"Bullying,\"

Question

5. The t test for two independent samples Two-tailed example Aa Aa "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 victims and a group of bully-victims using a 26-item, 3-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 25 victims scored an average of 25.3 with a sample standard deviation of 9 on the depression scale The group of 23 bully-victims scored an average of 20.5 with a sample standard deviation of 8 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: Ho: victims-ubully-victims = 0 H1 : victims-bully-victims * You conduct an independent-measures t test. Given your null and alternative hypotheses, this is a two-tailed test. To use the Distributions tool to find the critical region, you first need to set the degrees of freedom. The degrees of freedom is 47

Explanation / Answer

two-tailed test

46 degrees of freedom

+/- 2.687

Sp^2= (n1-1)S1^2+(n2-1)S2^2/(n1-1)+(n2-1)

         = (25-1)*9^2+(23-1)*8^2/24+22

         = 1944+1408/46

         = 72.86956

tSTAT=(X1-X2)-(µ1-µ2)/Sp^2(1/n1+1/n2)

  =(25.3-20.5)-0/72.86956(1/25+1/23)

=4.8/2.466 (SE)

=1.946472

The t statistic does not fall in the critical region. Therefore, null hypothesis is not rejected. You cannot conclude that victimes have a different mean depression score than bully-victims. Thus, it can be said that these two means are not different from one another.

  

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