Question

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Consider the experimental results for the following randomized block design. Make the calculations necessary to set up the analysis of variance table.

		Treatments
		A	B	C
Blocks	1	10	9	8
	2	12	7	5
	3	18	15	14
	4	20	18	18
	5	8	7	8

Use α = 0.05 to test for any significant differences.

State the null and alternative hypotheses.

H₀: μ_A ≠ μ_B ≠ μ_C
H_a: μ_A = μ_B = μ_C

H₀: Not all the population means are equal.
H_a: μ_A = μ_B = μ_C   

H₀: μ_A = μ_B = μ_C
H_a: μ_A ≠ μ_B ≠ μ_C

H₀: μ_A = μ_B = μ_C
H_a: Not all the population means are equal.

H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that the means of the three treatments are not equal.

Do not reject H₀. There is not sufficient evidence to conclude that the means of the three treatments are not equal.   

Do not reject H₀. There is sufficient evidence to conclude that the means of the three treatments are not equal.

Reject H₀. There is not sufficient evidence to conclude that the means of the three treatments are not equal.

Answer 1

from excel": data -data analysis: ANOVA without replication

Source of Variation	SS	df	MS	F	P-value
block	304.4	4	76.1	41.14	0.000
treatment	25.2	2	12.6	6.81	0.019
Error	14.8	8	1.85
Total	344.4	14

H₀: μ_A = μ_B = μ_C
H_a: Not all the population means are equal.

value of the test statistic =6.81

p-value =0.019

Reject H₀. There is sufficient evidence to conclude that the means of the three treatments are not equal.