I would be happy to help. Lets start with the experiment itself.
You are going to want to start with the ball at a particular height. You are going to repeat this several times so you will want the height to always be the same but fairly high so that the ball has some good bounces. You might want to try several different heights to determine what height you believe will work best (you don't want too many bounces or too few). It would probably work easiest to have your brother stand on a chair (don't forget to hold on to him!).
From the specific height you have chosen, your brother will drop the ball. Don't have him throw the ball. If he throws the ball it will add an additional energy to it every time that won't be consistent. If he just drops the ball then the starting energy will always be proportional to the height of the ball times gravity.
Now have him drop the ball several times from this height on a cement floor and several times on a tile floor and count the bounces. Doing the experiment several times will account for any slight differences between measurements (bounces).
For the experiment that is all you will need to do. I should mention that there may be other variables which could change things. For example, if it is cold outside and the concrete is outside, the rubber on the basketball will be cold and it will bounce differently than on the tile inside. You will want to keep everything as close to the same as possible during the experiment. The only thing you want to have change is the floor that the ball will bounce on (use the same ball and make sure it has plenty of air in it). (Of course he can always do hardwood floors and such.) Also keep in mind that the tile floors have grouted areas and if the ball hits these it won't bounce the same and might not even go in the same direction!
So the basic physics of what is happening is rather interesting. There are two types of energy that you will be playing with. The first is potential energy. So when the ball is at some height it has the "potential" to fall because of gravity. The second is kinetic energy which is the energy something has when it is in motion. When your brother is holding the ball it has only potential energy because it is not moving. As it falls the potential energy decreases and the kinetic energy increases. At the floor the potential energy (for our purposes) is zero. The ball hits the floor and looses some energy to the floor. (This is the Newton law thing ... for every action there is an equal and opposite reaction ... however the floor is much much bigger than the wall so the energy lost to the floor is not visible.) The ball bounces off the floor and goes up. As it increases it loses kinetic energy and gains potential energy until it is at the top of the bounce. Then it happens all over again. So that the total amount of energy is conserved (when you include the energy lost to the floor). This is how roller coasters work!
So the energy lost to the floor is different depending on the type of floor and the ball will lose more or less energy and as a result will bounce either less or more, respectively! This is a very basic explanation and hopefully will be enough to guide you through the explanation to your brother. Of course we are always here if you need a little more guidance on the explanation part.
As for references (aka. bibliography):
The first one is for an actual science project to build a roller coaster. It is aimed at older students but it has good references at the bottom of the page and will give you a little more explanation of kinetic and potential energy.
https://www.sciencebuddies.org/science- ... p037.shtml
These two just present the ideas of potential and kinetic energy and one, in fact, talks about how to do a ball dropping experiment!
http://jersey.uoregon.edu/vlab/PotentialEnergy/
http://www.eia.doe.gov/kids/energyfacts ... nergy.html
Good luck and we are here if you need any more help!
Heidi