An analysis of variance experiment produced a portion of the accompanying ANOVA table. (You may find it useful to reference the F table.)
a. Specify the competing hypotheses in order to determine whether some differences exist between the population means.
H_{0}: μ_{A} = μ_{B} = μ_{C} = μ_{D}; H_{A}: Not all population means are equal.
H_{0}: μ_{A} ≥ μ_{B} ≥ μ_{C} ≥ μ_{D}; H_{A}: Not all population means are equal.
H_{0}: μ_{A} ≤ μ_{B} ≤ μ_{C} ≤ μ_{D}; H_{A}: Not all population means are equal.
b. Fill in the missing statistics in the ANOVA table. (Round intermediate calculations to at least 4 decimal places. Round "MS" to 4 decimal places and "F" to 3 decimal places.)

c. At the 1% significance level, what is the conclusion to the test?
Do not reject H_{0}; we cannot conclude that some means differ.
Reject H_{0}; we can conclude that some means differ.
Reject H_{0}; we cannot conclude that some means differ.
Do not reject H_{0}; we can conclude that some means differ.
a)
The null and alternative hypothesis is
H_{0}: μ_{A} = μ_{B} = μ_{C} = μ_{D}; H_{A}: Not all population means are equal.
b)
ANOVA  
Source of variation  SS  df  MS  F  pvalue 
Between groups  16.94  3  5.6467  4.0443  0.0108 
Within groups  87.96  63  1.3962  
Total  104.9  66 
c)
Level of significance = 0.01
Pvalue = 0.0108
Pvalue > 0.01 we fail to reject null hypothesis.
Conclusion: Do not reject H_{0}; we cannot conclude that some means differ.
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