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Answer:
True. See explanation below
Step-by-step explanation:
Previous concepts
Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".
The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"
If we assume that we have groups and on each group from
we have
individuals on each group we can define the following formulas of variation:
And we have this property
The degrees of freedom for the numerator on this case is given by where k represent the number of groups.
The degrees of freedom for the denominator on this case is given by .
And the total degrees of freedom would be
And the we can find the F statistic