### Abstract:

This dissertation concerns two topics in the analysis of finite population surveys:
setting sample size and hypothesis testing. The first concerns the a priori determination
of the sample size needed to obtain species members. The second concerns
testing distributional hypotheses when two equal-size populations are sampled.
Setting sample size to obtain species is a problem which arises when an investigator
wants to obtain (1) a member of all species present in an area (2) a member of all
species whose relative frequency is greater than, say, 20% or (3) a member of each
species in a target set of species. Chapter 2 presents a practical solution to these
questions by setting a target sample size for which the species are obtained with
known probability. The solution requires the estimated relative frequency of the
rarest species of interest; total number of species is not needed. Because this problem
has substantial computational demands, easy-to-compute formulas are needed and
given. Three practical examples are presented.
Testing of finite population distributional hypotheses is covered in Chapter 3. The
test proposed here works under reasonably general designs and is based on a Horvitz-Thompson type correction of the usual Mann-Whitney U statistic. The investigation
here compared this proposed test to a corrected (for finiteness) form of the usual
Wilcoxon rank sum test. Size and power of the two test procedures are investigated
using simulation. The proposed test had approximately correct nominal size over a
wide range of situations. The corrected Wilcoxon test exhibited extreme violations
in size in many cases. Power of the two tests in situations where they have equal size
is similar in most practically interesting cases.