Question

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 Adults Seniors Sample Size X 107 2.00 255 3.30 3 13 3.09 32 2.83 1.57 1.68 1.69 1.86 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. Calculate the test statistic. (Round your answer to two decimal places.) What can be said about the P-value for this test? P-value > 0.100 0.050 < P-value < 0.100 0 0.010 < P-value < 0.050 0.001 CP value < 0.010 OP-value < 0.001 What can you conclude? Fail to reject . There is convincing evidence that the mean social marginality scores are not the same for all four age groups. Fail to reject Ho. There is not convincing evidence that the mean social marginality scores are not the same for all four age groups. Reject W. There is not convincing evidence that the mean social marginality scores are not the same for all four age groups Reject Ho. There is convincing evidence that the mean social marginality scores are not the same for all four age groups

Answer 1

Group	ni	x̅i	S2i	ni*(Xi-Xgrand)2	SS
1	107	2.000	2.46	104.661	261.2794
2	255	3.300	2.82	24.662	716.8896
3	313	3.090	2.86	3.192	891.1032
4	32	2.830	3.46	0.809	107.2476
	grand mean=	2.989	Total	133.3247	1976.5198
				SSTr	SSE
Source	SS	df	MS	F
Treatment	133.3247	3	44.4416	15.8068
error	1976.5198	703	2.8116
total	2109.8445	706

from above F =15.81

OP-value < 0.001

Reject He. There is convincing evidence that the mean social marginality scores are not the same for all four age groups