Question

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	6	5
	3	18	15	14
	4	20	18	18
	5	8	7	9

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

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

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.

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 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.

Answer 1

Applying 2 way ANOVA":

from above:

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

value of the test statistic. =4.98

p-value =0.039

since p value <0.05

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