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 pvalue to four decimal places.)
Source of Variation 
Sum of Squares 
Degrees of Freedom 
Mean Square 
F  pvalue 

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.
H_{0}: μ_{1} ≠
μ_{2} ≠ μ_{3}
H_{a}: μ_{1} =
μ_{2} =
μ_{3}H_{0}:
μ_{1} = μ_{2} =
μ_{3}
H_{a}: μ_{1} ≠
μ_{2} ≠
μ_{3} H_{0}:
Not all the population means are equal.
H_{a}: μ_{1} =
μ_{2} =
μ_{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}: μ_{1} =
μ_{2} = μ_{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 pvalue. (Round your answer to four decimal places.)
pvalue =
State your conclusion.
Reject H_{0}. There is 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 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.
Get Answers For Free
Most questions answered within 1 hours.