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. Sample mean Sample variance Sample standard deviation Plant 1 Atlanta 84 76 83 77 72 88 80 35.6 5.97 Plant 2 Dallas 71 76 72 75 68 82 74 23.6 4.86 Plant 3 Seattle 60 64 63 69 75 59 65 36.4 6.03

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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.
Sample
mean
Sample
variance
Sample
standard
deviation
Plant 1 Plant 2
Atlanta Dallas
84
76
83
77
72
88
80
35.6
5.97
71
76
72
75
68
82
74
23.6
4.86
Plant 3
Seattle
60
64
63
69
75
59
65
36.4
6.03
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. Sample mean Sample variance Sample standard deviation Plant 1 Plant 2 Atlanta Dallas 84 76 83 77 72 88 80 35.6 5.97 71 76 72 75 68 82 74 23.6 4.86 Plant 3 Seattle 60 64 63 69 75 59 65 36.4 6.03
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
Treatments
Error
Total
Sum
of Squares
480 X
Ho: M₁ = M₂ = μ3
На: M1 # M2 # M3
X
2
Degrees
of Freedom
Ho: M₁ M₂ M3
На: M1 = M2 = M3
15
17
Hỏ: At least two of the population means are equal.
Ha: At least two of the population means are different.
Ho: M₁ = M₂ = μ3
Ha: Not all the population means are equal.
Mean
Square
Test for any significant difference in the mean examination score for the three plants. Use α = 0.05.
State the null and alternative hypotheses.
Ho: Not all the population means are equal.
Ha: M₁ = M₂ = μ3
X
F
p-value
Transcribed Image Text: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 Treatments Error Total Sum of Squares 480 X Ho: M₁ = M₂ = μ3 На: M1 # M2 # M3 X 2 Degrees of Freedom Ho: M₁ M₂ M3 На: M1 = M2 = M3 15 17 Hỏ: At least two of the population means are equal. Ha: At least two of the population means are different. Ho: M₁ = M₂ = μ3 Ha: Not all the population means are equal. Mean Square Test for any significant difference in the mean examination score for the three plants. Use α = 0.05. State the null and alternative hypotheses. Ho: Not all the population means are equal. Ha: M₁ = M₂ = μ3 X F p-value
Expert Solution
Step 1

The given data is

  Plant 1 Atlanta Plant 2 Dallas Plant 3 Seattle
  84 71 60
76 76 64
  83 72 63
  77 75 69
  72 68 75
  88 82 59
Sample mean 80 74 65
Variance 35.6 23.6 36.4
Sample standard deviation 5.97 4.86 6.03

Here we perform the one-way ANOVA.

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