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

H0: μ1 ≠ μ2≠ μ3

H0: μ1 = μ2 = μ3

H0: M1 = M2 = M3

H0: M1 ≠ M2≠ M3

H0: μ1> μ2> μ3

H0: μ1 ≤ μ2≤ μ3

B) The alternative hypothesis is

There are no significant differences among the three treatment means

all pairs of means are significantly different from each other

There is at least one significant mean difference: At least two means significantly differ from each other

H1: μ1 ≠ μ2≠ μ3

C) The Critical F-value is:

Note: Leave the two decimal places after the decimal point

D)The F-statistic is:

Note: If it is a decimal number with two or more than two places, leave only two decimal places after the decimal point and do not round.

F) Your decision is

Reject the null hypothesis and conclude that there are no significant mean differences among the treatments

Reject the null hypothesis and conclude that there are significant mean differences among the treatments

Fail to reject the null hypothesis and conclude that there are no significant mean differences among the treatments

Fail to reject the null hypothesis and conclude that there are significant mean differences among the treatments

Answer 1

from above:

Group	ni	x̅i		ni*(Xi-Xgrand)2	(ni-1)*S2i
1	6	4		6.000	30.00
2	6	5		0.000	35.00
3	6	6		6.000	40.00
	grand mean=	5.0000		12.0000	105.00
				SSTr	SSE
Source	SS	df	MS	F	Fcrit
between	12.000	2	6.0000	0.857	3.6823
within	105.000	15	7.0000
total	117.000	17

A)

H0: μ1 = μ2 = μ3

B)

There is at least one significant mean difference: At least two means significantly differ from each other

C)

The Critical F-value is =3.68

D)

The F-statistic is: =0.86

E)

Fail to reject the null hypothesis and conclude that there are no significant mean differences among the treatments