Question

An experiment has been conducted for four treatments with seven blocks. Complete the following analysis of variance table. (Round your values for mean squares and F to two decimal places, and your p-value to three decimal places.)

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
Treatments	900
Blocks	200
Error
Total	1,600

Use α = 0.05 to test for any significant differences.

State the null and alternative hypotheses.

H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.H₀: Not all the population means are equal.
H_a: μ₁ = μ₂ = μ₃ = μ₄    H₀: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄
H_a: μ₁ = μ₂ = μ₃ = μ₄H₀: μ₁ = μ₂ = μ₃ = μ₄
H_a: Not all the population means are equal.H₀: μ₁ = μ₂ = μ₃ = μ₄
H_a: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄

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

Answer 1

>> The analysis of variance table:

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F Statistic	p value
Treatments	900	3	300	9.00	0.001
Blocks	200	6	33.33
Error	500	18	27.78
Total	1600	27

>> The null and alternative hypotheses:

H0: μ1 = μ2 = μ3 = μ4
Ha: Not all the population means are equal.

>> The value of the test statistic = 9.00

>> The p-value = 0.001

>> Conclusion: Reject H0. There is sufficient evidence to conclude that the means of the four treatments are not all equal.