Anova Question (two-way ANOVA -with replication) 2) The following table show the standardized math scores for...

Anova Question (two-way ANOVA -with replication)

2) The following table show the standardized math scores for a random sample of students for three states. The sample included an equal number of eight-graders and fourth-graders.

	Tennessee	Florida	Arizona
Eight Grade	260	292	286
	255	260	274
	247	287	290
	267	280	269
	253	275	284
	260	260	297
Fourth Grade	275	270	286
	248	283	290
	250	280	295
	221	260	278
	236	283	258
	240	290	287

Perform two-way ANOVA (with replication) using α = 0.10 by defining Factor A as the state and Factor B as to whether the student was an eighth-grader or a fourth-grader.
Test the effects that the state and the grade of the student have on the standardized math score
State sources of variation within sample .

SS

df

MS

F

P-value

F crit

Expert Solution

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Answer:

SUMMARY	Tenessee	Florida	Arizona	Total
Eighth grade
Count	6	6	6	18
Sum	1552	1654	1700	4906
Average	258.6667	275.6667	283.3333	272.5556
Variance	104.2667	181.0667	106.2667	227.6732

fourth grade
Count	6	6	6	18
Sum	1470	1676	1694	4840
Average	245	279.3333	282.3333	268.8889
Variance	323.2	63.06667	173.0667	468.2222

Total
Count	12	12	12
Sum	3022	3330	3394
Average	251.8333	277.5	282.8333
Variance	245.2424	114.6364	127.2424


ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Factor B	121	1	121	0.76346	0.389189	6.038134
Factor A	6592.889	2	3296.444	20.79921	2.15E-06	4.469551
Interaction	482.6667	2	241.3333	1.522715	0.234503	4.469551
Error	4754.667	30	158.4889

Total	11951.22	35

From the above ANOVA table, we find that Factor B is significant as the p-value (0.39) > 0.10 LOS

orchestra answered 2 years ago

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