An experiment was conducted to compare the effects of four different
chemicals, \(\mathrm{A}, \mathrm{B}, \mathrm{C},\) and \(\mathrm{D},\) in
producing water resistance in textiles. A strip of material, randomly selected
from a bolt, was cut into four pieces, and the four pieces were randomly
assigned to receive one of the four chemicals, \(\mathrm{A}, \mathrm{B},
\mathrm{C},\) or \(\mathrm{D} .\) This process was replicated three times, thus
producing a randomized block design. The design, with moistureresistance
measurements, is as shown in the figure (low readings indicate low moisture
penetration). Analyze the experiment using a method appropriate for this
randomized block design. Identify the blocks and treatments, and investigate
any possible differences in treatment means. If any differences exist, use an
appropriate method to specifically identify where the differences lie. What
are the practical implications for the chemical producers? Has blocking been
effective in this experiment? Present your results in the form of a report.
$$$
\begin{aligned}
&\text { Blocks (bolt samples) }\\\
&\begin{array}{|c|c|c|}
\hline 1 & 2 & 3 \\
\hline \mathrm{C} & \mathrm{D} & \mathrm{B} \\
9.9 & 13.4 & 12.7 \\
\mathrm{A} & \mathrm{B} & \mathrm{D} \\
10.1 & 12.9 & 12.9 \\
\mathrm{B} & \mathrm{A} & \mathrm{C} \\
11.4 & 12.2 & 11.4 \\
\mathrm{D}_{2} & \mathrm{C} & \mathrm{A} \\
12.1 & 12.3 & 11.9
\end{array}
\end{aligned}
$$
