Question

3. The t test for two independent samples- Two-tailed example AaAa? Bullying," according to noted expert Dan Olweus, "poisons the educational environment and affects the leaning 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 a 26-item, 3-point depression scale. Assume scores on the depression scale are normaly distributed and that the variances of the depression scores are the same among bully-victims and bystanders. The group of 30 bully-victims scored an average of 21.5 with a sample standard deviation of 10 on the depression scale. The group of 27 bystanders scored an average of 25.8 with a sample standard deviation of 9 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: Pbuly-victims Pbystanders-0 You conduct an independent-measures t test. Given your null and alternative hypotheses, this is atwo-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 55 Degrees of Freedom 55 2500 4.0 3.0 2.0 1.0 0.0 1.0 2.0 3.0 0.679 0.000 067 The critical t-scores that form the boundaries of the critical region for ? 0.01 are 2.668 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(Mu -Mz)- The t statistic is The t statistic in the critical 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

Answer 1

s_p² = ((n1 - 1)s1^2 + (n2 - 1)s2^2)/(n1 + n2 - 2)

      = (29 * (10)^2 + 26 * (9)^2)/(10 + 9 - 2)

     = 294.47

SE = sqrt(s_p² /n1 + s_p² /n2)

       = sqrt(294.47/30 + 294.47/27)

       = 4.552

The test statistic t = (M1 - M2)/SE

                            = (21.5 - 25.8)/4.552 = -0.94

THe t-statistic lies in the critical region, therefore null hypothesis is not rejected.

the two means are not different from each other.