Aaron,

 Surely you gest.  I agree five is a small sample size but small samples
are not necessarily invalid. Small sample sizes are precisely what
statistics are meant to analyse.  In fact, large sample sizes (I have
data at work that is data collected every second for 2 or more weeks)
demand several caveats. In fact, some typical control charts and other
measures i.e. CpK can not be validly done.  One must remember that
Demming and others did their stuff in the 1920's and 1930's....when data
was collected and plotted manually!  Their methods by default used small
sample sizes because nobody had the time to hand calculate anything
more. In fact, several tables in my stat books provided by AT&T as
adapted from Shewhart only go to sample size of 20.  That is why the
polling agencys can use slightly over 1000 adult americans to get valid
poll results.  1000 is only 0.0004% of the approx. 250 million
americans.  Five bees out of a hive of 60,000 is 0.0083%.  This is a
much larger sample than we get in our political polls, etc.  Smaller
sample sizes do have a higher margin of error but what really drives the
sample size in the consistancy of varience (square of the standard
deviation) of the data.  If you can say for sure that if a bee is
infected or anything else that you want to measure can be detected 100%
of the time then you can reduce sample size.  Also, the level of
confidence or power that you want to have in your conclusion will drive
sample size.  If you want to be 99% sure, then your sample size will be
larger than if you only want to be 95% 90% or even 80% given the same
variance.  If you ignore sample size you may increase your risk of
making a Type I or a Type II error.  A Type I error occurs when you say
the null hypothesis is rejected or not true, when in fact it is true.  A
Type II error occurs when you say the null hypothesis is not rejected
when it is false.  This type of error is more common in small sample
size data as you do not have the data to determine if in fact there is a
statistically significant difference.  I am just offering my two cents
here.  I have not looked at the questions specific to these last
postings

Cordially,

Jeff Holbrook
Corning, NY