A few years ago, Penn State put out a brochure concerning tracheal mites
and sampling statistics.  The question posed was, if I cut a bee and find
or don't find mites, then cut another, etc.  HOW MANY BEES DO I HAVE TO CUT
before I DECIDE THAT I DON'T HAVE TO CUT ANY MORE.

In other words, if you cut five bees and they all have mites, do you need
to dissect any more bees to determine whether you have a mite problem?  Or,
if you cut 5 bees and none have mites, can you stop?

They did a lot of work on this.  However, the bottom line was that the Penn
state study simply verified basic statistics - the results came out just as
one would predict.  Somewhere, I have some Tables from a very old stat
book.  It let's you look up sample size and the power of the test in order
to answer this same question.

I'd have to go digging, but I can tell you that as a general rule, the
power of the test improves through a sample of 25 (bees, light bulbs,
etc.).  Then you hit the old issue of diminishing returns.  The amount of
improvement in the power or reliability of the test begins to fall off
rapidly between 25 and 30, and sample sizes over 30 don't add much for the
time invested.  Now, this generalization assumes lots of things about
normal distributions, representative samples, and other issues - so it
won't hold for all estimates -- but its not a bad rule of thumb.