You may need to use the appropriate technology to answer this 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 


86  70  58  
74  74  64  
83  74  62  
76  73  68  
72  68  74  
89  91  76  
Sample mean 
80  75  67 
Sample variance 
48.4  67.2  49.2 
Sample standard deviation 
6.96  8.20  7.01 
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.
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.
You may need to use the appropriate technology to answer this question.
The following data are from a completely randomized design. In the following calculations, use 𝛼 = 0.05.
Treatment 1 
Treatment 2 
Treatment 3 


63  83  70  
46  71  55  
54  87  61  
37  67  50  
x_{j} 
50  77  59 
s_{j}^{2} 
123.33  90.67  74.00 
(a)
Use analysis of variance to test for a significant difference among the means of the three treatments.
State the null and alternative hypotheses.
Find the value of the test statistic. (Round your answer to two decimal places.)
Find the pvalue. (Round your answer to three decimal places.)
pvalue =
State your conclusion.
(b)
Use Fisher’s LSD procedure to determine which means are different.
Find the value of LSD. (Round your answer to two decimal places.)
LSD =
Find the pairwise absolute difference between sample means for each pair of treatments.
x_{1} − x_{2}
=
x_{1} − x_{3}
=
x_{2} − x_{3}
=
Which treatment means differ significantly? (Select all that apply.)