Consider an experiment to examine the influence of product
packaging on consumer preference.  They considered two factors,
package type (A=cylindrical, B=rectangular, C=conic) and shape
(X=tall, Y=regular, Z=squat).  The response is a measure of consumer
preference score.  This score is a combination of several measurements
and can be assumed to be normally distributed.  According to design,
each consumer was given only one of the 9 objects (the factor
combinations of 3 types and 3 shapes). \\
(a) Write out (in words or symbols) an appropriate model for this
experiment, including assumptions. \\
(b) Construct an appropriate summary
table.  Be sure to arrange it to best display the results. \\
(c) Construct an interaction plot for these data.  Annotate it (by
hand or by computer) with a measure for multiple comparison among the
factor combinations. \\
(d) Conduct formal inference for these data.  \\
(e) Interpret results, referring to both formal analysis and table or
graphical summaries.

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2. Another company decided to do a similar experiment, for the same
reason and with the same factors.  However, they decided to use fewer
consumers and give each one all the products.  Repeat steps (a--e) for
this experiment.

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3. Name the experimental designs used in problems 1 and 2.  Compare
these two designs.  Under what circumstances might each be preferred?
Be concise, limiting your answer to less than half a page.
