Sound engineers studied factors that might affect the output (in decibels) of a rock concert speaker system. The results of their ANOVA tests are shown (some information is missing). $$\begin{array} { l r r l r l }
\hline \text { Source of Variation } & { S S } & d f & M S & F & P \text {-value } \
\hline \text { Amplifier } & 99.02344 & & 99.02344 & & 0.005718 \
\text { Position } & 93.98698 & & 31.32899 & 3.215807 & 0.051003 \
\text { Interaction } & 10.15365 & 3 & 3.384549 & 0.347412 & 0.791505 \
\text { Error } & 155.875 & 16 & 9.742188 & & \
\
\text { Total } &359.0391 & 23& & & \
\hline
\end{array}$$ Which is the number of amplifiers and positions tested?
A)1, 3
B)2, 4
C)3, 5
D)4, 1

Question

Sound engineers studied factors that might affect the output (in decibels) of a rock concert speaker system. The results of their ANOVA tests are shown (some information is missing). $$\begin{array} { l r r l r l } 
\hline \text { Source of Variation } &  { S S } & d f & M S & F & P \text {-value } \
\hline \text { Amplifier } & 99.02344 & & 99.02344 & & 0.005718 \
\text { Position } & 93.98698 & & 31.32899 & 3.215807 & 0.051003 \
\text { Interaction } & 10.15365 & 3 & 3.384549 & 0.347412 & 0.791505 \
\text { Error } & 155.875 & 16 & 9.742188 & & \
\
\text { Total } &359.0391 & 23& & & \
\hline
\end{array}$$ Which is the number of amplifiers and positions tested?
A)1, 3
B)2, 4
C)3, 5
D)4, 1

Quizplus · Accepted Answer

According to the ANOVA table, there are two sources of variation: Amplifier and Position. The Amplifier factor has only one degree of freedom, which means that there was only one level of Amplifier tested. The Position factor has three degrees of freedom, which means that there were four levels of Position tested (since df= n-1). Therefore, the answer is B) 2, 4.

Sound Engineers Studied Factors That Might Affect the Output (In