For a class project, students tested four different brands of laundry detergent (1, 2, 3, 4) in
three different water temperatures (hot, warm, cold) to see whether their were any
differences in how well the detergents could clean clothes. The students took 36 identical
pieces of cloth and made them dirty by staining them with coffee, dirt, and grass. The 36
pieces were randomly assigned to the 12 combinations of detergent and temperature so
that each combination had 3 replicates. After washing, the students rated how clean the
clothes were from 0 (no change) to 20 (completely spotless). The two factor ANOVA table
is shown below along with an interaction plot and residual plots. $$\begin{array} { | l r r r r r | }
\hline \text { Source } & \text { df } & \begin{array} { c }
\text { Sums of } \
\text { Squares }
\end{array} & \begin{array} { l }
\text { Mean } \
\text { Square }
\end{array} & \text { F-ratio } & \text { P-value } \
\hline \text { Detergent } & 3 & 38.972 & 12.9907 & 3.966 & 0.0171 \
\text { Temp } & 2 & 181.056 & 90.5278 & 27.634 &

Question

For a class project, students tested four different brands of laundry detergent (1, 2, 3, 4) in
three different water temperatures (hot, warm, cold) to see whether their were any
differences in how well the detergents could clean clothes. The students took 36 identical
pieces of cloth and made them dirty by staining them with coffee, dirt, and grass. The 36
pieces were randomly assigned to the 12 combinations of detergent and temperature so
that each combination had 3 replicates. After washing, the students rated how clean the
clothes were from 0 (no change) to 20 (completely spotless). The two factor ANOVA table
is shown below along with an interaction plot and residual plots. $$\begin{array} { | l r r r r r | } 
\hline \text { Source } & \text { df } & \begin{array} { c } 
\text { Sums of } \
\text { Squares }
\end{array} & \begin{array} { l } 
\text { Mean } \
\text { Square }
\end{array} & \text { F-ratio } & \text { P-value } \
\hline \text { Detergent } & 3 & 38.972 & 12.9907 & 3.966 & 0.0171 \
\text { Temp } & 2 & 181.056 & 90.5278 & 27.634 & < 0.0001 \
\text { Error } & 30 & 98.278 & 3.2759 & & \
\text { Total } & 35 & 318.306 & & & \
\hline
\end{array}$$ 
  
a. Write the hypotheses tested by the Detergent F-ratio. Test the hypotheses and explain
your conclusion in the context of the problem.
b. Write the hypotheses tested by the Temp F-ratio. Test the hypotheses and explain your
conclusion in the context of the problem.
c. Check the conditions required for the ANOVA analysis.

Quizplus · Accepted Answer

The Answer of For a class project, students tested four different brands of laundry detergent (1, 2, 3, 4) in
three different water temperatures (hot, warm, cold) to see whether their were any
differences in how well the detergents could clean clothes. The students took 36 identical
pieces of cloth and made them dirty by staining them with coffee, dirt, and grass. The 36
pieces were randomly assigned to the 12 combinations of detergent and temperature so
that each combination had 3 replicates. After washing, the students rated how clean the
clothes were from 0 (no change) to 20 (completely spotless). The two factor ANOVA table
is shown below along with an interaction plot and residual plots. $$\begin{array} { | l r r r r r | } 
\hline \text { Source } & \text { df } & \begin{array} { c } 
\text { Sums of } \
\text { Squares }
\end{array} & \begin{array} { l } 
\text { Mean } \
\text { Square }
\end{array} & \text { F-ratio } & \text { P-value } \
\hline \text { Detergent } & 3 & 38.972 & 12.9907 & 3.966 & 0.0171 \
\text { Temp } & 2 & 181.056 & 90.5278 & 27.634 & < 0.0001 \
\text { Error } & 30 & 98.278 & 3.2759 & & \
\text { Total } & 35 & 318.306 & & & \
\hline
\end{array}$$ 
  
a. Write the hypotheses tested by the Detergent F-ratio. Test the hypotheses and explain
your conclusion in the context of the problem.
b. Write the hypotheses tested by the Temp F-ratio. Test the hypotheses and explain your
conclusion in the context of the problem.
c. Check the conditions required for the ANOVA analysis.

For a Class Project, Students Tested Four Different Brands of Laundry