How many scientists does it take to change a lightbulb?

At least two, so that they know the results can be replicated.
Okay, that's not really a funny joke, but watching the show Modern Family on ABC the other night reminded me of an academic exercise my advisor used to have us teach the undergrads in his integrative biology course.  On the show, one of the characters, Phil, is driven crazy by a smoke alarm that won't stop beeping.  After changing the batteries in all of the smoke detectors in the house, the beeping continues.  In the end, he discovers that he was replacing the old batteries with other batteries that he thought were new, but were really low on juice themselves (or something along those lines).
This brings us to the thought experiment of changing a light bulb.  The problem is a common one: you walk into a room and flip the light-switch, but the light does not come on.  Assuming the whole of the system consists of a power source (the electricity in your house), a circuit (the wiring in the walls), a switch, and the light bulb, how would you go about testing whether or not the lightbulb has gone bad?  (Oh yeah, and assume that the lightbulb is one of those old school painted incandescent bulbs where you can't see the filament).  A normal person (i.e. non-scientist) would say, just change the bulb out with a new one, and it should work.  And they might be right.  BUT, if the new bulb doesn't work, then what do you do?  The most common answer when I taught this lesson in class was "call an electrician".  Which sounds sensible, BUT, as the point of the lesson was, a scientific approach to the problem may save you the hefty cost of an electrician (and teach you a little something about how scientists see the world, and why we are such sticklers for properly controlled experiments).  For example, how would you feel if you paid $80 or $100 for an electrician to come out and tell you that there was a defect in the new bulb you bought from the store, and simply tried another bulb and it worked.  Or, how would you feel after paying that bill only to find out that it really wasn't the bulb, but a "short" circuit that allowed the electrician's new bulb to work for a little while, but then stop working as soon as he left and you paid the bill?  How could this all be avoided? Simple, by actually testing the bulb.  And how one would do that is by setting up a positive control, that is, a situation where you can be relatively certain that if the bulb is in working condition, it will work.  What I mean by this, is that you must take into account the entire system within which you are working.  In this case, you have 4 components: the power supply, the circuit, the switch, and the lightbulb.  A defect in any of these 4 things could cause the light not to work.  The first hypothesis is that the lightbulb has burned out.  This is a good hypothesis since observations and experience teach us that burned out lightbulbs are a fairly common occurrence.  However, as we have seen, the test of replacing the lightbulb only works if we get a positive result (that is the new lightbulb works), BUT, we are at a complete loss if the new bulb does NOT work.  If that happens, then we still have no idea whether the problem lies in the power supply, the circuit, the switch, or the light bulb (even though it is new, and we assume it should work, there may be a factory defect, or it may have been damaged in shipping, etc. etc.)  To test the lightbulb hypothesis, a scientist would go to another room in the house where he or she is reasonably sure the light works.  Then he or she would flip the switch, and verify that the light in this other room does indeed work.  Once it has been verified, the scientist now has a positive control.  That is, he or she should be able to take the lightbulb from the other room that didn't work, put it into this new socket and, if the lightbulb is still functional then it should work.  If it does not work in this other room (and assuming the scientist then switches out the bulbs again, and the one that originally worked in this socket still works) then the scientist can now conclude that the bulb is broken.  However, this still doesn't answer the question of whether or not the remaining components in the system are still in working order (as it is possible that there could be a problem with the switch and the bulb, or the circuit and the bulb, or any combination of two or more things that could all go wrong at the same time).  However, if you have a working circuit (and working bulb) in the other room, you now have the means to test whether or not some other component of the system is faulty.  You do this by taking the bulb that worked in the other room, and placing it into the socket of the circuit that was not working.  If this bulb does not work (and you go back and test it again in the other circuit and it still does) then you can conclude that something else must be wrong and it is time to call the electrician.  However, if this bulb does work, then, you can rest (relatively) assured that a new bulb (so long as it is not defective) will work in the circuit. This may seem like a lot of work just to change a light bulb, but if you have ever done science, you have probably learned long ago how much time and effort the proper controls can save you (in addition to giving you certainty about your results), and if you haven't, well, I hope you never find yourself replacing a lightbulb only to find that the new one still doesn't work.  Or, if you do, I hope you remember this post, and it helps out, even if only a little bit.