In the study "The Use of Regression Analysis for Correcting Matrix Effects in the X-Ray Fluorescence Analysis of Pyrotechnic Compositions," published in the Proceedings of the Tenth Conference on the Design of Experiments in Army Research Development and Testing, ARO-D Report $65-3(1965),$ an experiment was conducted in which the concentrations of four components of a propellant mixture and the weights of fine and coarse particles in the slurry were each allowed to vary. Factors $A, B, C,$ and $D,$ each at two levels, represent the concentrations of the four components, and factors $E$ and $F,$ also at two levels, represent the weights of the fine and coarse particles present in the slurry. The goal of the analysis was to determine if the X-ray intensity ratios associated with component 1 of the propellant were significantly influenced by varying the concentrations of the various components and the weights of the particles in the mixture. A $\frac{1}{8}$ fraction of a $2^{6}$ factorial experiment was used, with the defining contrasts being $A D E, B C E$, and $A C F$. The data shown here represent the total of a pair of intensity readings. The pooled mean square error with 8 degrees of freedom is given by $0.02005 .$ Analyze the data using a 0.05 level of significance to determine if the concentrations of the components and the weights of the fine and coarse particles present in the slurry have a significant influence on the intensity ratios associated with component $1 .$ Assume that no interaction exists among the six factors.
$$
\begin{array}{clc}
& \text { Treatment } & \text { Intensity } \\
\text { Batch } & \text { Combination } & \text { Ratio Total } \\
\hline 1 & \text { abef } & 2.2480 \\
2 & \text { cdef } & 1.8570 \\
3 & \text { (1) } & 2.2428 \\
4 & \text { ace } & 2.3270 \\
5 & \text { bde } & 1.8830 \\
6 & \text { abcd } & 1.8078 \\
7 & \text { adf } & 2.1424 \\
8 & \text { bcf } & 1.9122
\end{array}
$$