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. Hoi Hyouths young Adults Adults Seniors H: at least two of the four u/'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. Source of Variation Treatments Error The given summary statistics are below. Sample Size x S Age Group Youths Young Adults 244 113 Degrees of Freedom 2.00 1.48 k-1 N-k 3.70 1.78 Sum of Squares Mean Square SST MSTO k-1 307 3.18 SST Adults Seniors 1.58 SSE 48 2.72 1.98 SSEMSE N-k F MST F=msir MSE 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 k4 and k-1-[ The value of N is the total number of observations in the data set, so we have N= 113 +244 + 307 +48 [ Thus, the degrees of freedom for Error is N-k- degrees of freedom for Treatments.