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 show 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 Plant 3 Seattle Dallas 84 70 59 75 74 64 81 73 61 75 73 69 71 68 76 94 86 61 80 74 65 68.8 39.6 41.2 Sample mean Sample

MATLAB: An Introduction with Applications
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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 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 2 Plant 3
Plant 1
Atlanta
Dallas
Seattle
84
70
59
75
74
64
81
73
61
75
73
69
71
68
76
94
86
61
Sample
mean
80
74
65
Sample
68.8
39.6
41.2
variance
Sample
standard 8.29
6.29
6.42
deviation
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
Sum
Degrees
Mean
F
p-value
of Squares of Freedom
Square
of Variation
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.
OH₁₂H₁₂ = H₂ = H₂
H: Not all the population means are equal.
ⒸH₁ H₂ H₂ H3
OH,: Not all the population means are equal.
H₂H₂ = H₂ = 13
OH₁₂¹ H₂ = H₂ = H₂
OH: At least two of the population means are equal.
H₂: At least two of the population means are different.
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.
O Do not reject H. There is sufficient evidence to conclude that the means for the three plants are not equal.
O Do not reject H. There is not sufficient evidence to conclude that the means for the three plants are not equal.
O Reject H. There is not sufficient evidence to conclude that the means for the three plants are not equal.
O Reject H. There is sufficient evidence to conclude that the means for the three plants are not equal.
Transcribed Image Text: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 2 Plant 3 Plant 1 Atlanta Dallas Seattle 84 70 59 75 74 64 81 73 61 75 73 69 71 68 76 94 86 61 Sample mean 80 74 65 Sample 68.8 39.6 41.2 variance Sample standard 8.29 6.29 6.42 deviation 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 Sum Degrees Mean F p-value of Squares of Freedom Square of Variation 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. OH₁₂H₁₂ = H₂ = H₂ H: Not all the population means are equal. ⒸH₁ H₂ H₂ H3 OH,: Not all the population means are equal. H₂H₂ = H₂ = 13 OH₁₂¹ H₂ = H₂ = H₂ OH: At least two of the population means are equal. H₂: At least two of the population means are different. 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. O Do not reject H. There is sufficient evidence to conclude that the means for the three plants are not equal. O Do not reject H. There is not sufficient evidence to conclude that the means for the three plants are not equal. O Reject H. There is not sufficient evidence to conclude that the means for the three plants are not equal. O Reject H. There is sufficient evidence to conclude that the means for the three plants are not equal.
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