Question

#2

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	105	253	313	32
x	2.00	3.10	3.06	2.82
s	1.58	1.66	1.69	1.87

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

α = 0.01.

Calculate the test statistic. (Round your answer to two decimal places.)

F =

Answer 1

from given data:

Group	ni	x̅i		ni*(Xi-Xgrand)2	SS=(ni-1)*s2
1	105	2		86.026	259.6256
2	253	3.1		9.606	694.4112
3	313	3.06		7.505	891.1032
4	32	2.82		0.232	108.4039
	grand mean=	2.905		103.3690	1953.5439
				SSTr	SSE
Source	SS	df	MS	F	Fcrit
Treatment	103.3690	3	34.456	12.3289	3.810
error	1953.5439	699	2.7948
total	2056.9129	702

from above test statistic F =12.33

since test statistic is higher than critical value , we reject null and conclude that the mean social marginality scores are not the same for all four age groups