I'm preparing to propose a topic for my master's thesis and want to
look at college admissions applications.  I'm looking at students who
were accepted to the college. The three variables I'm using will be:
--The applicants intented major
--The discount rate given to the applicant (discount rate is the
percentage of tuition costs accounted for by institutional financial
aid)
--Whether or not they chose to enroll (conversion)

I want to see if there is a relationship between major and conversion
rate and discount rate.  My "guess" is that some niche/specialized
programs will have high conversion rates despite having similar
discount rates when compared to other programs.

In the end, I anticipate a data table that will resemble the following:
              MEAN DISCOUNT    STD. DEV OF    CONVERSION
MAJOR            RATE            DISC. RATE     RATE
-----------   -------------    ------------   ----------
Business         0.497            1.23           0.591
RIAP             0.491            1.19           0.825
English          0.512            1.39           0.527

What/how should I do prepare my statistical tests to properly decide
whether or not there is a significant difference?

Do you have the raw data for conversions or only the rate?  The same
with the discount rate.

I will end up having raw data for both conversions and discount
rate... (still waiting for the data file from our institutional
research office).

Well... off the top of my head it looks like you have a generalized
(logistic) mixed effects model

You also have factors for each major.... your model would look like this

f(conv) = Sum ( MC_i  + MN_i) + C + e

f(.) is the function for logistic regression
Where MC is a constant for the major
MN is a normal with mean 0 and variance MV_i^2
C is the overall constant 
e is the error term.

To do your test you would need to test between the MC_i's... 

if the test said MC_i = MC_j then the conversion rates would be the same... 
if your test said that MC_i /not = MC_j you have different conversion rates.

I should add for the model... there is basically an indicator... ie..
for someone in Major i... you only use MC_i and MN_i... not the other
ones