Educating on the Scientific Method

I am a Junior at California Polytechnic University, Pomona, majoring in Philosophy. In a few weeks I will be conducting a science demonstration before a class of High School Seniors as a part of a service learning project for my study of the Philosophy of Science.

My background in science is not very strong, so I was looking for some help in figuring out what would be a good demo. The basic goal (backed up by a presentation the previous day and group discussion immediately following) is to show how the scientific method, used correctly, does not always work in the way most students think that it does. I.e., the progression is not always observation-->hypothesis-->observation-->accept or reject hypothesis.

What I would like to illustrate, in a simple demonstration, that an observation (experiment) that does not match the hypothesis (theory) does not always mean the theory is to be discarded. I want to illustrate an instance where, as is commonly the case, an unexpected result does not necessarily mean bad theory, but the wrong experiment.

The demonstration must be concrete and easy to conduct in around 20 minutes. It must use inexpensive materials, or materials commonly found in a lab. The class is a chemistry class, but experiments in biology or physics are fair game in this instance.

Does anyone have any ideas?