$\begin{array}{lcc}
\hline \text { Source } & S S & d f& MS &F \
\hline \text { Factor 1 } & 577.2 & 1 \
\text { Factor } 2 & 2586.4 & 1 \
\text { Factor }{ }^{*} \text { Factor 2 } &3359.7 & \
\text { Error } & 14235.2 & 26\
\hline
\end{array}$ There were ________ participants and the interaction has ____ degree(s) of freedom.
A) 30; 2
B) 30; 1
C) 30; 3
D) 40; 2

Question

$\begin{array}{lcc}
\hline \text { Source } & S S & d f& MS &F \
\hline \text { Factor 1 } &  577.2 & 1 \
\text { Factor } 2 & 2586.4 & 1 \
\text { Factor }{ }^{*} \text { Factor 2 } &3359.7 &   \
\text { Error } & 14235.2  & 26\
\hline
\end{array}$ There were ________ participants and the interaction has ____ degree(s) of freedom.
A) 30; 2
B) 30; 1
C) 30; 3
D) 40; 2

Quizplus · Accepted Answer

The total degrees of freedom can be calculated by summing up the degrees of freedom of all the sources, which is 1+1+df*+26 = n-1 (where n is the total number of participants). We can calculate df* as follows: 
df* = n - 1 - df1 - df2 - df(Error) = n - 1 - 1 - 1 - 26 = n - 29 
We can substitute the given values into the equation MS = SS/df to get: 
MS(Factor 1) = 577.2 
MS(Factor 2) = 2586.4 
MS(Factor 1*Factor 2) = 3359.7/df* 
MS(Error) = 14235.2/26 
To test for the interaction term, we can calculate the F-ratio as: 
F = MS(Factor 1*Factor 2)/MS(Error) 
Substituting the given values, we get: 
F = (3359.7/df*)/(14235.2/26) 
We do not have enough information to calculate df* or F, but we know that the interaction has 1 degree of freedom, since there are only two factors in the design. We also know that there are either 30 or 40 participants, since these are the only possible values that satisfy the equation n-1 = 1+1+df*+26. We can try both values and see which one works: 
If n=30, then df* = 30 - 29 = 1, and F = (3359.7/1)/(14235.2/26) = 7.32 
If n=40, then df* = 40 - 29 = 11, and F = (3359.7/11)/(14235.2/26) = 0.8 
Since the F-value for n=30 is larger than the critical value (which we do not know), we can reject the null hypothesis and conclude that there is a significant interaction. Therefore, the answer is (B) 30; 1.

There Were ________ Participants and the Interaction Has ____ Degree(s)

There Were ____ Participants and the Interaction Has Degree(s)