**6. 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 anxiety in a group of victims and a group of bully-victims using a 26-item, 3-point anxiety scale. Assume scores on the anxiety scale are normally distributed and that the variances of the anxiety scores are the same among victims and bully-victims.The group of 30 victims scored an average of 21.5 with a sample standard deviation of 10 on the anxiety scale. The group of 27 bully-victims 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 victims or bully-victims will be more anxious, so you formulate the null and alternative hypotheses as:\( H_0: \mu_{\text{victims}} - \mu_{\text{bully-victims}} = 0 \)\( H_1: \mu_{\text{victims}} - \mu_{\text{bully-victims}} \neq 0 \)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. The degrees of freedom is ________. ### Understanding Critical t-Scores and Calculating the t Statistic**Critical t-Scores:**The critical t-scores that form the boundaries of the critical region for α = 0.01 are ± ________.**Calculating the t Statistic:**To calculate the t statistic, you first need to determine the standard error under the assumption that the null hypothesis is true. Here's a step-by-step guide:1. **Calculate the Pooled Variance:** The pooled variance is denoted by \( s_p^2 = \) ________.2. **Determine the Standard Error:** The standard error of the difference in means is calculated as: \[ s_{(M1 - M2)} = \text{________} \]3. **Compute the t Statistic:** Once the standard error is found, the t statistic can be calculated as: \[ \text{The t statistic is} \, \text{________} \]**Interpreting the t Statistic:**1. **Compare the t Statistic to the Critical Region:** The t statistic ________ in the critical region.2. **Conclusion on the Null Hypothesis:** Therefore, the null hypothesis is ________. 3. **Final Interpretation:** You ________ conclude that victims have a different mean anxiety score than bully-victims. Thus, it can be said that these two means are ________ different from one another.This process and interpretation help in understanding whether there is a statistically significant difference between the groups' means.

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Given Information: Given information regarding two sample one for victims and another for…

Math

Statistics

In order to calculate thet 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 poole wariance is s The standard error is s(M1 - M2) = The t statistic is The t statistic in the critical region. Therefore, the null hypothesis is You conclude that victims have a different mean anxiety score than bully-victims. Thus, it can be said that chese two means are different from one another.

In order to calculate thet 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 poole wariance is s The standard error is s(M1 - M2) = The t statistic is The t statistic in the critical region. Therefore, the null hypothesis is You conclude that victims have a different mean anxiety score than bully-victims. Thus, it can be said that chese two means are different from one another.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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