Question

The statistics on test scores for 4 groups are given below.. Test the hypothesis that the means for each group are equal. Use a .01 significance level

	fresh	soph	jr.	sr
mean	88	90	78	92
var	120	150	200	250
n	9	9	9	9

NB: Please i will like it to be cleared for someone who is learning it by herself . I saw similar answer online but i cant figure out how they come about the (Sum of Sq, DF, Mean Square, & F for the Source, Between and within) Pls i need what and what number they use to get each figure.

Thanks

Answer 1

from above:

	ni	x̅i	S2i	ni*(Xi-Xgrand)2	(ni-1)*S2i
Fresh	9	88.000	120.000	9.000	960.00
Soph	9	90.000	150.000	81.000	1200.00
Jr.	9	78.000	200.000	729.000	1600.00
Sr.	9	92.000	250.000	225.000	2000.00
	grand mean=	87.000		1044.000	5760.00
				SSTr	SSE
as MS=SS/df and F=MS(treatment)/MS(error)
Source of variation		SS	df	MS	F
between		1044.00	3	348.00	1.933
within		5760.00	32	180.00
total		6804.00	35

for 0.01 level and (3,32) df ; crtiical value =4.46

for test statsistic 1.933 is not higher then crtiical value we fail to reject null hypothesis

we do not have evidence to conclude at 0.01 level to conclude that means for each group are unequal.