Question

5. A nonparametric procedure for two independent samples - A large sample case Aa Aa E "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 and are also victims (bully-victims). You decide to compare anxiety in a group of 52 bully-victims and a group of 48 bystanders using a 26-item, 3-point anxiety scale. You are concerned that the anxiety scores from bully-victims and bystanders may not satisfy the assumptions for a parametric test. Since n1 = 52 and n2 = 48 are both greater than 20, you decide that the most appropriate nonparametric procedure to use is the To do this procedure, you rank-order all 100 scores and select bystanders as the group to compute the sum of the ranks. The sum of the ranks for bystanders is 2,162. The expected sum of the ranks for this group, Rexp = The Zobt for the rank sums statistic is Use the Distributions tool to answer the questions that follow and decide whether to reject the null hypothesis, Ho: There is no systematic difference between the anxiety scores of bully-victims and the anxiety scores of bystanders. Standard Normal Distribution Mean = 0.0 Standard Deviation = 1.0 OOO aan -2 NW . The With a = .01, the region of rejection is defined as a z-score greater than or less than Z-score for the rank sums statistic the region of rejection. The correct decision is to null hypothesis. the

Answer 1

sample size n1		group 1	48
sample size n2		group 2	52

sample mean =

μ=n1(n1+n2+1)/2=

2424

You are concerned that the anxiety scores from bully-victims and bystanders may not satisfy the assumptions for a parametric test. Since ni = 52 and n2 = 48 are both greater than 20, you decide that the most appropriate nonparametric procedure to use is the Rank sum test To do this procedure, you rank-order all 100 scores and select bystanders as the group to compute the sum of the ranks. The sum of the ranks for bystanders is 2,162. The expected sum of the ranks for this group, Rexp = 2424

Variance=	σ2=n1n2(n1+n2+1)/12=		21008.00
standard deviation= σ =			144.94

test stat z=

Z=(U-μ)/σ

=

-1.81

. The With a = .01, the region of rejection is defined as a z-score greater than 2.58 Z-score for the rank sums statistic is not in the region of rejection. TI null hypothesis. or less than -2.58 ecision is to fail to reject the