A firm is concerned with variability in hourly output at several factories and shifts. Here are the results of an ANOVA using output per hour as the dependent variable (some information is missing). $$\begin{array} { | l | c | c | c | c | }
\hline \text { Source } & \text { Sum of Squares } & d f & \text { Mean Square } & \text { FRatio } \
\hline \text { Factory } & 19012.5 & 1 & 19012.5 & 26.427 \
\hline \text { Shift } & 258.333 & 2 & 129.167 & 0.180 \
\hline \text { Factory*Shift } & 80908.333 & 2 & 40454.167 & 56.230 \
\hline \text { Error } & 8633.333 & 12 & 719.444 & \
\hline \text { Total } & 108812.5 & 17 & 6400.735 & \
\hline
\end{array}$$ The number of observations in each treatment cell (row-column intersection) is:
A)1.
B)2.
C)3.
D)impossible to determine.

Question

A firm is concerned with variability in hourly output at several factories and shifts. Here are the results of an ANOVA using output per hour as the dependent variable (some information is missing). $$\begin{array} { | l | c | c | c | c | } 
\hline \text { Source } & \text { Sum of Squares } & d f & \text { Mean Square } & \text { FRatio } \
\hline \text { Factory } & 19012.5 & 1 & 19012.5 & 26.427 \
\hline \text { Shift } & 258.333 & 2 & 129.167 & 0.180 \
\hline \text { Factory*Shift } & 80908.333 & 2 & 40454.167 & 56.230 \
\hline \text { Error } & 8633.333 & 12 & 719.444 & \
\hline \text { Total } & 108812.5 & 17 & 6400.735 & \
\hline
\end{array}$$ The number of observations in each treatment cell (row-column intersection) is:
A)1.
B)2.
C)3.
D)impossible to determine.

Quizplus · Accepted Answer

The degrees of freedom for the Factory and Shift factors are 1 and 2, respectively. Since the total number of observations is 17 and there are two factors, the remaining observations (17 - 3 - 2 = 12) must be distributed evenly across the six treatment cells. Therefore, each treatment cell has 2 observations, implying that there are 3 treatments in each factor.

A Firm Is Concerned with Variability in Hourly Output at Several