Question: Is it possible to use the accelerometer to detect height? For instance, if I'm holding the phone on my hand and then detect the height after raising my arm?

Thanks

Answer: 
Assuming you mean you want to detect the height the phone was raised from its staring point, yes. The android accelerometer measures force, more info on how to use it can be found [here](http://developer.android.com/reference/android/hardware/SensorEvent.html#values). Keep in mind that the accelerometer isn't a perfect device, and so your results will be approximations of how much the phone was really moved.
Yes, bt you need to integrate the output twice and add in the two integration constants - initial velocity and displacement.

Rgds,
Martin