If you google “relationship between exercise and sleep” you’ll find a lot of research has been done in this area. So, the first thing you’d want to do is find a unique aspect that hasn’t been studied yet.
Have you ever designed a study or taken statistics? In order to do a meaningful study, you’ll need to come up with a testable hypothesis with little variation between your control group and your test group except the exercise intervention. And before you start, it’s wise to do some estimations to determine how many subjects you need, and how big enough of a difference your experiment will make in others’ sleep habits, in order to reach a statistically significant conclusion.
It depends on the study. Some studies last as little as few weeks and others go on for many years. Are you and an Exercise Physiologist?
Usually when setting up a study you will need to have standards in place (or establish new ones) depending what you are looking to get out of the study. As for studies done regarding sleep and exercise you should be able to find plenty online with some good search. In my opinion these type of studies are not that conclusive for the simple reason everyone is different and there are so many factors that come into play that would make any such study difficult to validate. hopefully someone here can give you a better answer than mine. I’m not an expert on sleeping, I only know how my own body reacts to sleep (or lack of it). Here is a recent post from IDEA:
I hope this helps.