Your project seems to be based on mathematics (probability) and/or behavioral science.
So, for research, I'd suggest doing Google searches to find out (or working out mathematically) how likely it is that two people would have the same birthday and how likely it is for a given number of people in a group to have the same birthdays. What about people whose birthdays are February 29? And so on. Try to think of different parts of this problem that you could learn about.
You could also do some searches on whether people with certain birthdays or birthdays in certain months / seasons tend to act certain ways- though I'm not sure if any such research has been done, I think that you'll run across some interesting theories that you might be able to incorporate into a hypothesis. Maybe people with summer birthdays tend to go to the shortest lines and thus be in the front more, for example.
In general, the research section contains background information that might help judges and other interested people understand your project. Try to add the information that you think will be helpful and relevant, but remember to keep it concise! A long, wall-of-text background can confuse readers.
Good luck, and hope this helped!
Nature uses only the longest threads to weave her patterns, so that each small piece of her fabric reveals the organization of the entire tapestry.