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 71 59 75 76 65 81 74 62 76 73 69 71 70 75 85 86 60 Sample mean 79 75 65 Sample variance 35 6 33 6 37 2 Sample standard deviation 5 97 5 80 6 10 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 0 05 State the null and alternative hypotheses H 0 1 2 3 H a 1 2 3 H 0 At least two of the population means are equal H a At least two of the population means are different H 0 Not all the population means are equal H a 1 2 3 H 0 1 2 3 H a 1 2 3 H 0 1 2 3 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 H 0 There is sufficient evidence to conclude that the means for the three plants are not equal Do not reject H 0 There is not sufficient evidence to conclude that the means for the three plants are not equal Reject H 0 There is not sufficient evidence to conclude that the means for the three plants are not equal Do not reject H 0 There is sufficient evidence to conclude that the means for the three plants are not equal

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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

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	71	59
75	76	65
81	74	62
76	73	69
71	70	75
85	86	60
Sample mean	79	75	65
Sample variance	35.6	33.6	37.2
Sample standard deviation	5.97	5.80	6.10

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

= 0.05.

State the null and alternative hypotheses.H₀: ₁ = ₂ = ₃ H_a: ₁ ₂ ₃H₀: At least two of the population means are equal. H_a: At least two of the population means are different.