Question

Part of an ANOVA table is shown below.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F
Between Treatments	64			8
Within Treatments (Error)			2
Total	100

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If we want to determine whether or not the means of the populations are equal, the p-value is

	a.	greater than .1.
	b.	between .05 to .1.
	c.	between .025 to .05.
	d.	less than .01.

Answer 1

Source of	Sum of	Degrees	Mean	F
Variation	Squares	of Freedom	Square
Between Treatments	64	4	16	8
Within Treatments (Error)	36	18	2
Total	100

Sum of squares of errors = Total sum of squares - Sum of squares between treatments = 100-64 =36

Degrees of freedom of errors = Sum of squares of errors / Mean square errors

= 36/2 = 18

Mean square between treatments = Mean square errors * F = 2*8 = 16

Degrees of freedom between treatments = Sum of squares between treatments / Mean square between treatments

= 64/16 = 4

p-value (Using excel function) = =F.DIST(x,deg_1,deg_2,cumulative) =F.DIST(8,4,18,FALSE) = 0.0005 (less than 0.01) Option d