Question

The following data were obtained from an independent-measures research study comparing three treatment conditions.

I	II	III
n = 6	n = 4	n = 4
M = 2	M = 2.5	M = 5	N = 14
T = 12	T = 10	T = 20	G = 42
SS = 14	SS = 9	SS = 10	ΣX2tot = 182

Use an ANOVA with α = .05 to determine whether there are any significant mean differences among the treatments.

A) The null hypothesis in words is

There are no significant differences among the three treatment means.

There is at least one significant mean difference among the three treatment means.

All the pairs of means significantly differ from each other

There are no significant differences between the means of groups 1 and 2

B) The alternative hypothesis in symbols is

H1: μ1 ≠ μ2≠ μ3

H1: M1 ≠ M2≠ M3

H1: μ1 = μ2 = μ3

H1: M1 = M2 = M3

In Anova, we do not state the alternative hypothesis in symbols

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 not significant differences among the conditions

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

Fail to reject the null hypothesis and conclude that there are not significant differences among the conditions

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

Answer 1

Group	ni	x̅i		ni*(Xi-Xgrand)2	(ni-1)*S2i
1	6	2		6.000	14.00
2	4	2.5		1.000	9.00
3	4	5		16.000	10.00
	grand mean=	3.0000		23.0000	33.00
				SSTr	SSE
Source	SS	df	MS	F	Fcrit
between	23.000	2	11.5000	3.833	3.9823
within	33.000	11	3.0000
total	56.000	13

A)

There are no significant differences among the three treatment means.

B)

In Anova, we do not state the alternative hypothesis in symbols

C)

Critical F-value is =3.98

D)

The F-statistic is =3.83

F)Fail to reject the null hypothesis and conclude that there are not significant differences among the conditions