The accompanying summary statistics for a measure of social marginality for samples of youths, young adults, adults, and seniors appeared in the paper €œPerceived Causes of Loneliness in Adulthood€ (Journal of Social Behavior and Personality [2000]: 67€“84). The social marginality score measured actual and perceived social rejection, with higher scores indicating greater social rejection. 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 score is not the same for all four age groups? Test the relevant hypotheses using a = .01.

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Young Age Group Youths Adults Adults Seniors 36 2.00 3.40 3.07 2.84 1.56 1.68 1.66 1.89 Sample Size 106 255 314