Question

In an experiment designed to test the output levels of three different treatments, the following results were obtained: SST = 320, SSTR = 130,

n_T = 19.

Set up the ANOVA table. (Round your values for MSE and F to two decimal places, and your p-value to four decimal places.)

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
Treatments
Error
Total

Test for any significant difference between the mean output levels of the three treatments. Use

α = 0.05.

State the null and alternative hypotheses.

H₀: Not all the population means are equal.
H_a: μ₁ = μ₂ = μ₃H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.    H₀: μ₁ = μ₂ = μ₃
H_a: Not all the population means are equal.H₀: μ₁ ≠ μ₂ ≠ μ₃
H_a: μ₁ = μ₂ = μ₃H₀: μ₁ = μ₂ = μ₃
H_a: μ₁ ≠ μ₂ ≠ μ₃

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

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

p-value =

State your conclusion.

Do not 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.    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

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

Level of Significance : = 0.05

Anova table :

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
Treatments	130	K - 1 = 3-1 = 2	65	5.4737	0.015446
Error	190	- K = 16	11.875
Total	320	- 1 = 18

Here, Mean Square = Sum of Squares / Degrees of freedom
F =  Mean Square of Treatment / Mean Square of error
And p-value is obtained from the F tables.

Since p-value < 0.05, we reject H₀ and conclude that there is sufficient evidence to conclude that the means of the three treatments are not equal.

Hope this answers your query!