Question

A company manufactures printers and fax machines at plants located in Atlanta, Dallas, and Seattle. To measure how much employees at these plants know about quality management, a random sample of 6 employees was selected from each plant and the employees selected were given a quality awareness examination. The examination scores for these 18 employees are shown in the following table. The sample means, sample variances, and sample standard deviations for each group are also provided. Managers want to use these data to test the hypothesis that the mean examination score is the same for all three plants.

	Plant 1 Atlanta	Plant 2 Dallas	Plant 3 Seattle
	86	70	59
	75	75	63
	83	72	62
	75	73	70
	71	70	75
	78	84	73
Sample mean	78	74	67
Sample variance	31.2	27.6	42.8
Sample standard deviation	5.59	5.25	6.54

Set up the ANOVA table for these data. (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 in the mean examination score for the three plants. Use

α = 0.05.

State the null and alternative hypotheses.

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

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

H₀: μ₁ = μ₂ = μ₃
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

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 sufficient evidence to conclude that the means for the three plants are not equal.

Do not reject H₀. There is not sufficient evidence to conclude that the means for the three plants are not equal.    

Reject H₀. There is sufficient evidence to conclude that the means for the three plants are not equal.

Reject H₀. There is not sufficient evidence to conclude that the means for the three plants are not equal.

Answer 1

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