Question

consider the following table:

	ss	df	ms	f
error			626.7
total	12825.12	18

step 5 of 8: what is the sum of squares of sample means about the grand mean? please round your answer to two decimal places.
answer
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Explanation:

Step1: Recall the relationship in ANOVA

In ANOVA, the sum - of - squares total ($SS_{total}$) is the sum of the sum of squares among treatments ($SS_{among}$) and the sum of squares error ($SS_{error}$), i.e., $SS_{total}=SS_{among}+SS_{error}$. We want to find $SS_{among}$, and we know that $SS_{total} = 12825.12$ and $SS_{error}$ can be calculated from the mean - square error ($MS_{error}$) and degrees of freedom error ($DF_{error}$). But we can also directly use the fact that the sum of squares of sample means about the grand mean is the sum of squares among treatments.
We know that $MS_{among}=\frac{SS_{among}}{DF_{among}}$, and we are given $DF_{among} = 6$ and $MS_{among}=884.12$.

Step2: Calculate $SS_{among}$

Using the formula $SS_{among}=MS_{among}\times DF_{among}$, we substitute the given values: $SS_{among}=884.12\times6$.
$SS_{among}=5304.72$

Answer:

$5304.72$