Golf Ball Data

The following data was collected by a statistics professor who lives
adjacent to a golf course and found out after moving that his back yard
was a prime location for receiving golf balls poorly hit by 
amatuer golfers.  

Golf balls are usually labeled by brand and with a number (1, 2, 3, or 4).
The professor was curious to know if each of these numbers was equally likely
among golfs balls hit poorly by golfers.  (The fancy term for this is 
"uniformly distributed".)  Anyway, here is a tally of the first 500 golf
balls that landed in his yard:

ball number      1       2        3        4        other
tally           137     138      107      104       14


So what is the verdict?  Clearly the numbers 1-4 did not occur with
exactly equal frequency in this sample, but is the distribution far
enough from uniform to conclude that something besides random chance
is going on here?

In order to answer this, we need some measure of how far this distribution
is from uniform.  Come up with several reasonable ways to measure this,
and compute each of them for the sample above.  Such a measure is often
called a "test statistic" because it is computed from the data in order
to "test" whether or not something seems to be the case.













What we really want to know (for one or more of the measures above) is how
unusual the value is for our sample.  One way to get some idea about this
is to have a computer simulate 486 golf balls (we'll just ignore the "other")
drawn from a uniform distribution.  If we do such a simulation a number of 
times we can record how often the resulting measure is as extreme as or more
extreme than the measure for our sample data.

We will do this simulation (for at least one proposed measure) using Minitab.