Question

consider the following table:

	ss	df	ms	f
error			622.89
total	8917.39	19

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.
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Explanation:

Step1: Recall the relationship in ANOVA table

The sum - of - squares (SS) in ANOVA has the relationship $SS_{Total}=SS_{Among Treatments}+SS_{Error}$. We want to find $SS_{Among Treatments}$, which is the sum of squares of sample means about the grand mean.

Step2: Rearrange the formula

We know that $SS_{Among Treatments}=SS_{Total}-SS_{Error}$. The degrees of freedom (DF) for total is $DF_{Total}=19$, the degrees of freedom for among - treatments is $DF_{Among Treatments}=8$, and the mean - square for among - treatments is $MS_{Among Treatments} = 258.2$. The mean - square for error is $MS_{Error}=622.89$. We are given $SS_{Total}=8917.39$. First, we need to find $SS_{Error}$. Since $MS_{Error}=\frac{SS_{Error}}{DF_{Error}}$, and $DF_{Error}=DF_{Total}-DF_{Among Treatments}=19 - 8=11$, then $SS_{Error}=MS_{Error}\times DF_{Error}=622.89\times11 = 6851.79$.

Step3: Calculate $SS_{Among Treatments}$

$SS_{Among Treatments}=SS_{Total}-SS_{Error}=8917.39 - 6851.79=2065.60$

Answer:

$2065.60$