Question

Given the following sample information, test the hypothesis that the treatment means are equal at the 0.01 significance level:

Treatment 1	Treatment 2	Treatment 3
3	9	6
2	6	3
5	5	5
1	6	5
3	8	5
1	5	4
	4	1
	7	5
	6
	4

a. State the null hypothesis and the alternative hypothesis.

H₀ : μ₁ =  μ₂   = μ₃

H₁ : Treatment means are not all the same.

b. What is the decision rule? (Round the final answer to 2 decimal places.)

Reject H₀ if F > 5.78.

c. Compute SST, SSE, and SS total. (Round the final answers to 2 decimal places.)

SST = ___

SSE = ___

SS total = ___  
d. Complete the ANOVA table. (Round the SS, MS, and F values to 2 decimal places.)

	Source	SS	DF	MS	F
	Factor		2
	Error		21
	Total		23

e. State your decision regarding the null hypothesis.

Decision: Do not reject H_0.

f.Find the 95% confidence interval for the difference between treatment 2 and 3. (Round the final answers to 2 decimal places.)

95% confidence interval is: ___ ± ___  

We can conclude that the treatments 2 and 3 are different.

Answer 1

CONSTRUCTION OF ANOVA TABLE
				VARIANCE RATIO
SOURCE OF VARIATION DUE TO	d.f	S.S	M.S.S	Fcal	Fcri
TREATMENT	2	46.96	23.48	9.30	19.44
ERROR	21	53.00	2.52
TOTAL	23	99.96

Since Fcal < Fcri; So we Accept H0 at 5% Level of Significant.

Therefore we conclude that " The Effect of Treatments are Homogeneous".

NOTE: The Fcri value is Extracted from the tabulated value of F. In the see the instersection value of (2, 20-24), we will get 19.44 and 19.45.