“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 bystanders 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 bystanders. 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 bystanders 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 bystanders will be more depressed, so you formulate the null and alternative hypotheses as: H00: μvictimsvictims – μbystandersbystanders = 0 H11: μvictimsvictims – μbystandersbystanders ≠ 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 . t Distribution Degrees of Freedom = 58

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section: Chapter Questions

Problem 8SGR

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2. The t test for two independent samples - Two-tailed example

“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 bystanders 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 bystanders.

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 bystanders 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 bystanders will be more depressed, so you formulate the null and alternative hypotheses as:

H00: μvictimsvictims – μbystandersbystanders	=	0
H11: μvictimsvictims – μbystandersbystanders	≠	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 .

t Distribution

Degrees of Freedom = 58

-4.0-3.0-2.0-1.00.01.02.03.04.0t

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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