Question

The following data were obtained for a randomized block design involving five treatments and three blocks: SST = 510, SSTR = 370, SSBL = 95. Set up the ANOVA table. (Round your value for 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
Blocks
Error
Total

Test for any significant differences. Use α = 0.05.

State the null and alternative hypotheses.

H₀: Not all the population means are equal.
H_a: μ₁ = μ₂ = μ₃ = μ₄ = μ₅H₀: μ₁ = μ₂ = μ₃ = μ₄ = μ₅
H_a: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄ ≠ μ₅    H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.H₀: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄ ≠ μ₅
H_a: μ₁ = μ₂ = μ₃ = μ₄ = μ₅H₀: μ₁ = μ₂ = μ₃ = μ₄ = μ₅
H_a: Not all the population means are equal.

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.

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

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

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

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

Answer 1

Solution;-

Source of Variation	Sum of squares	Degree of Freedom	Mean Square	F	p-value
Treatments	370	4	92.5	16.444	0.001
Blocks	95	2	47.5	8.4444	0.011
Error	45	8	5.625
Total	510	14

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

H_a: μ₁ = μ₂ = μ₃ = μ₄ = μ₅
H_a: At least two of the population means are different.

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Analyze sample data.

F statistics is given by:-

F = 16.444

The P-value = 0.001

Interpret results. Since the P-value (0.001) is less than the significance level (0.05), we have to reject the null hypothesis.

Conclusion:-

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