Question

Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 42 employees were randomly selected and randomly assigned to the three proposed methods in such a way that each method was used by 14 workers. The number of units assembled correctly was recorded, and the analysis of variance procedure was applied to the resulting data set. The following results were obtained: SST = 13,960; SSTR = 4,510.

(a)

Set up the ANOVA table for this problem. (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	?	?

(b)

Use α = 0.05 to test for any significant difference in the means for the three assembly methods.

State the null and alternative hypotheses.

H₀: μ₁ ≠ μ₂ ≠ μ₃
H_a: μ₁ = μ₂ = μ₃

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

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
H_a: μ₁ ≠ μ₂ ≠ μ₃

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

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

t stat =

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

p-value =

State your conclusion.

Do not reject H₀. There is not sufficient evidence to conclude that the means of the three assembly methods are not equal.

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

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

Do not reject H₀. There is sufficient evidence to conclude that the means of the three assembly methods are not equal.

Answer 1

(a)

The ANOVA Table isset up for the problem as follows:

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p - value
Treatments	4510	k - 1 = 3 - 1 = 2	4510/2 = 2255.00	2255.00/242.31 = 9.31	0.0005
Error	13960 - 4510 = 9450	N - k = 42 - 3 = 39	9450/39 = 242.31
Total	13960	N - 1 = 42 - 1 = 41

(b)

Correct option:

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

(c)

F stat = 2255.00/242.31 = 9.31

(d)

Degrees of Freedom for numerator = 2

Degrees of freedom for denominator = 39

By Technology, p - value = 0.0005

(e)

Correct option:

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