Question

An analysis of variance experiment produced a portion of the accompanying ANOVA table. (You may find it useful to reference the F table.)

a. Specify the competing hypotheses in order to determine whether some differences exist between the population means.

• H₀: μ_A = μ_B = μ_C = μ_D; H_A: Not all population means are equal.

• H₀: μ_A ≥ μ_B ≥ μ_C ≥ μ_D; H_A: Not all population means are equal.

• H₀: μ_A ≤ μ_B ≤ μ_C ≤ μ_D; H_A: Not all population means are equal.

b. Fill in the missing statistics in the ANOVA table. (Round intermediate calculations to at least 4 decimal places. Round "MS" to 4 decimal places and "F" to 3 decimal places.)

ANOVA
Source of Variation	SS	df	MS	F	p-value
Between Groups	16.94	3			0.0108
Within Groups	87.96	63
Total	104.90	66

c. At the 1% significance level, what is the conclusion to the test?

• Do not reject H₀; we cannot conclude that some means differ.

• Reject H₀; we can conclude that some means differ.

• Reject H₀; we cannot conclude that some means differ.

• Do not reject H₀; we can conclude that some means differ.

Answer 1

a)

The null and alternative hypothesis is

H₀: μ_A = μ_B = μ_C = μ_D; H_A: Not all population means are equal.

b)

ANOVA
Source of variation	SS	df	MS	F	p-value
Between groups	16.94	3	5.6467	4.0443	0.0108
Within groups	87.96	63	1.3962
Total	104.9	66

c)

Level of significance = 0.01

P-value = 0.0108

P-value > 0.01 we fail to reject null hypothesis.

Conclusion: Do not reject H₀; we cannot conclude that some means differ.