Question

The following data summarize the results from an independent measures study comparing three treatment conditions.

I	II	III
n = 6	n = 6	n = 6
M = 4	M = 5	M = 6	N = 18
T = 24	T = 30	T = 36	G = 90
SS = 30	SS = 35	SS = 40	ΣX2tot = 567

Use an ANOVA with α = .05 to determine whether there are any significant differences among the three treatment means

a) The null hypothesis in symbols is

b)The alternative hypothesis is

c)The Critical F-value is:

d)The F-statistic is:

e)Your decision is

Answer 1

Null and Alternative Hypothesis:

Ho: µ1 = µ2 = µ3

H1: At least one mean is different.

Number of treatment, k = 3

Total sample Size, N = 9

df(between) = k-1 = 2

df(within) = N-k = 6

df(total) = N-1 = 8

SS(between) = (Sum1)²/n1 + (Sum2)²/n2 + (Sum3)²/n3 - (Grand Sum)²/ N = 12

SS(within) = SS1 + SS2 + SS3 = 105

SS(total) = SS(between) + SS(within) = 117

MS(between) = SS(between)/df(between) = 6

MS(within) = SS(within)/df(within) = 17.5

Critical value Fc = F.INV.RT(0.05, 2, 6) = 5.143

F = MS(between)/MS(within) = 0.3429

Decision:

F < Fc, Do not reject the null hypothesis.

there is no significant differences among the three treatment means

ANOVA
Source of Variation	SS	df	MS	F	F crit
Between Groups	12	2	6	0.3429	5.1433
Within Groups	105	6	17.5
Total	117	8