a)
Generate 50 trial simulations from a one-way layout in a CRD with
$n_1=n_2=n_3=4$, $\sigma=1$ and $\mu_i=i,i=1,2,3$.  For each
simulation record the $SS_{MODEL}$ and $SS_{ERROR}$.  This can be
accomplished by using the program {\tt genss} which I wrote in
{\tt S}.  The easiest way to use this is as follows:

\begin{itemize}
\item
      import {\tt genss} into S by typing: \\
      {\tt S < \DIR/genss.s}
\item
      set up file {\tt hwk3.sin} with the lines: \\
  \begin{center}
  \begin{verbatim}
  genss()
  q()
  \end{verbatim}
  \end{center}
\item
run S in batch mode by typing: \\
  \begin{center}
  \begin{verbatim}
  S BATCH hwk3.sin hwk3.sout
  \end{verbatim}
  \end{center}
\item
The batch job may take several minutes or longer, though your prompt
will return immediately.  The batch job is finished when the last line
of {\tt hwk3.sout} is ``{\tt > q()}''
\end{itemize}

You may want to look at {\tt \DIR/genss.s}.  To verify that it does
what you think.  When completed, the file {\tt hwk2.sout} will contain 50 lines with
2 columns of sums of squares (and some other junk you will have to
edit out.  Of course, if you know {\tt S} and wish to proceed below
using it, you can save the results, e.g.\  {\tt ss <- genss()}.
\\ \\
b)
Plot histograms (or stemleaf diagrams) of $SS_{MODEL}$ and $SS_{ERROR}$.  For each, compare the 80\%,
90\% and 98\% points with the critical points of the appropriate
distribution.
\\
c)
Plot $SS_{MODEL}$ against $SS_{ERROR}$ (possibly using some
transformation).  Test whether or not they appear to be statistically
independent using what you learned in Stat 849.
\\
d) Plot a histogram of the $F$-statistic for equal means.  Compare
with 80\%, 90\% and 98\% points for the null ($H_o$) distribution and
comment on your findings.
