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Suppose the accompanying summary statistics for a measure of social marginality for samples of youths, young adults, adults, and seniors appeared in a research paper. The social marginality score measured actual and perceived social rejection, with higher scores indicating greater social rejection. Young Adulte Adults 246 Age Group Youths Sample Size x s 116 2.00 3.50 1.46 1.76 Adults Seniors 303 3.17 1.58 44 2.74 1.99 For purposes of this exercise, assume that it is reasonable to regard the four samples as representative of the U.S. population in the corresponding age groups and that the distributions of social marginality scores for these four groups are approximately normal with the same standard deviation. Is there evidence that the mean social marginality scores are not the same for all four age groups? Test the relevant hypotheses using a = 0.01.

Suppose the accompanying summary statistics for a measure of social marginality for samples of youths, young adults, adults, and seniors appeared in a research paper. The social marginality score measured actual and perceived social rejection, with higher scores indicating greater social rejection. Young Adulte Adults 246 Age Group Youths Sample Size x s 116 2.00 3.50 1.46 1.76 Adults Seniors 303 3.17 1.58 44 2.74 1.99 For purposes of this exercise, assume that it is reasonable to regard the four samples as representative of the U.S. population in the corresponding age groups and that the distributions of social marginality scores for these four groups are approximately normal with the same standard deviation. Is there evidence that the mean social marginality scores are not the same for all four age groups? Test the relevant hypotheses using a = 0.01.

MATLAB: An Introduction with Applications
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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Suppose the accompanying summary statistics for a measure of social marginality for samples of youths, young adults, adults, and seniors appeared in a research paper. The social marginality score measured actual and perceived social rejection, with higher scores indicating greater social rejection. Age Group Youths Young Adults Seniors Adults 246 Sample Size x 5 116. Treatments 2.00 1.46 Error Degrees Source of Variation of Freedom Sample Size x S The given summary statistics are below. Age Group Youths 3.50 For purposes of this exercise, assume that it is reasonable to regard the four samples as representative of the U.S. population in the corresponding age groups and that the distributions of social marginality scores for these four groups are approximately normal with the same standard deviation. Is there evidence that the mean social marginality scores are not the same for all four age groups? Test the relevant hypotheses using a = 0.01. 1.76 Step 1 A hypothesis test is to be conducted to determine if the mean social marginality scores are not the same for all four age groups. That is, the following hypotheses will be tested. Ho: youths young Adults Adults Seniors H.: at least two of the four a's are different Since we are told to assume that it is reasonable to regard the four samples as representative of the U.S. population in the corresponding age groups and that the distributions of social marginality scores for these four groups are approximately normal with the same standard deviation, the assumptions for the ANOVA test have been met. When performing an ANOVA test, a table is helpful to organize values in calculation of the test statistic and corresponding P-value. Recall the format of a partial ANOVA table, given below. 116 2.00 1.46 303 k-1 3.17 N-k 1.50 Young Adults 246 44 2.74 1.99 303 3.50 3.17 1.76 1.58 Sum of Squares Mean Square SSTr SSE Adults Seniors 44 2.74 1.99 F SST = MSTr F = MSTr MSE SSE-MSE N-k We will first focus on the column for Degrees of Freedom. The value of k is the number of populations being compared. Here, we are comparing the means of four age groups, so we have k-4 and k-1- The value of N is the total number of observations in the data set, so we have N116 +246 + 303 +44- Thus, the degrees of freedom for Error is N - k- degrees of freedom for Treatments.
Transcribed Image Text:Suppose the accompanying summary statistics for a measure of social marginality for samples of youths, young adults, adults, and seniors appeared in a research paper. The social marginality score measured actual and perceived social rejection, with higher scores indicating greater social rejection. Age Group Youths Young Adults Seniors Adults 246 Sample Size x 5 116. Treatments 2.00 1.46 Error Degrees Source of Variation of Freedom Sample Size x S The given summary statistics are below. Age Group Youths 3.50 For purposes of this exercise, assume that it is reasonable to regard the four samples as representative of the U.S. population in the corresponding age groups and that the distributions of social marginality scores for these four groups are approximately normal with the same standard deviation. Is there evidence that the mean social marginality scores are not the same for all four age groups? Test the relevant hypotheses using a = 0.01. 1.76 Step 1 A hypothesis test is to be conducted to determine if the mean social marginality scores are not the same for all four age groups. That is, the following hypotheses will be tested. Ho: youths young Adults Adults Seniors H.: at least two of the four a's are different Since we are told to assume that it is reasonable to regard the four samples as representative of the U.S. population in the corresponding age groups and that the distributions of social marginality scores for these four groups are approximately normal with the same standard deviation, the assumptions for the ANOVA test have been met. When performing an ANOVA test, a table is helpful to organize values in calculation of the test statistic and corresponding P-value. Recall the format of a partial ANOVA table, given below. 116 2.00 1.46 303 k-1 3.17 N-k 1.50 Young Adults 246 44 2.74 1.99 303 3.50 3.17 1.76 1.58 Sum of Squares Mean Square SSTr SSE Adults Seniors 44 2.74 1.99 F SST = MSTr F = MSTr MSE SSE-MSE N-k We will first focus on the column for Degrees of Freedom. The value of k is the number of populations being compared. Here, we are comparing the means of four age groups, so we have k-4 and k-1- The value of N is the total number of observations in the data set, so we have N116 +246 + 303 +44- Thus, the degrees of freedom for Error is N - k- degrees of freedom for Treatments.
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