A Machine Manufacturer Conducted a Study to Compare the Performance

Essay

A machine manufacturer conducted a study to compare the performance of two types of similar machines A and B in terms of the hardness of the product manufactured.According to the production supervisor,the machine setting (high,medium,low)also affects the hardness of the product.The hardness readings (response variable)are given in a two-factor factorial design format with two observations per cell. $\begin{array}{cc}&\text { Machine type }\\\text { Machine Setting }&\text { A } & \text { B } \\\text { Low }&8 & 4 \\&8 & 4 \\\\\text { Medium }&7 & 5 \\&6 & 2 \\\\\text { High }&9 & 4 \\&10 & 5\end{array}$ You are also given the following additional information:
SS (machine type)= 48,SS (machine setting)= 8,SST = 64
-Complete the following ANOVA Table and determine the value of the F statistic
$$\begin{array} { | l | c | c | c | c | } \hline \text { Source } & \text { SS } & \text { d.f. } & \text { MS } & \text { F } \\\hline \text { Treatment } & 583.39 & & & \\\hline \text { Error } & & & & \\\hline \text { Total } & & 1555.57 & & \\\hline\end{array}$$