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
	85	72	58
	75	74	65
	81	74	63
	77	73	68
	72	68	75
	84	89	61
Sample mean	79	75	65
Sample variance	26.8	52.0	35.6
Sample standard deviation	5.18	7.21	5.97

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: μ₁ = μ₂ = μ₃H₀: μ₁ = μ₂ = μ₃
H_a: μ₁ ≠ μ₂ ≠ μ₃    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.

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.

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

Answer 1