A professional real estate site analysis company was hired to survey
all the locations of a 75 unit restaurant chain, in an effort to
optimize future location selection criteria. Over 50 attributes
(freestanding, end-cap, square footage, traffic counts, visibility,
etc.) were evaluated, and based on that information, a sales
prediction matrix was created.

The 75 unit chain has 5 drive through locations. Of the top ten
overperforming stores (actual sales vs. predicted matrix sales), 4
were drive through. The 5th drive through location indexed very close
to predicted sales.

Question: Has drive through been proven mathematically significant to
the site selection criteria, and if so, how significant is it?

Please show your math and explain how you arrived at your decision. Thanks so much!

Have you read the FAQs about Google Answers' policy on homework assignments?

I work for this company. I regret if my wording of the problem makes
it look as if it is a homework assignment. I assure you this is quite
real and is something we are exploring right now. My gut feel is this
is very significant but this is based on experience, not math. The
sample size is small and that is my concern.

Not homework?  Maybe you should be writing textbooks.  OK, I'll fall for it.

Mathematically, the probability of seeing such an unexpected
arrangement of the data is statistically significant, assuming that
you are using the usual 0.05 cut-off for signficance.  The easiest way
to approach this problem is with a two-by-two table, or:

          Drive through    Not drive through
Top 10           4                 6
the rest         1                 64

There are many ways to evaluate this table, including both the Chi2
and Fisher's exact.  Chi2 is the standard method taught for 2x2
tables, but would not be ideal here, because one expects to find, on
the average, less than one drive-through in the top 10 performers, and
Chi2 should have at least 5 as an expected value.  So the Fisher's
exact would be preferred.

The p value is 0.0008, or very much less than 0.05.

Show the math?   No way.  The calculation requires multiple
factorials, with 75!the largest.  Just go to one of the many websites
that offer on-line Fisher's exact (such as
http://www.unc.edu/~preacher/fisher/fisher.htm) and put in your
numbers.  Just be sure not to put in 6,10,1,65.  The site also gives
you the formula, in case your are interested (you need to calculate
for this data set and add anything more extreme, i.e. all 5
drive-throughs showing up in the top 10).