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: 
Yes, bt you need to integrate the output twice and add in the two integration constants - initial velocity and displacement.

Rgds,
Martin
First of all you measure Linear acceleration and gravity together (also some noise)
So it means when you are using accelerometer you will get
Accelerometer Readings = Linear Acc. + Gravity + Noise
Here you just only need Linear Acc. but the Accelerometer reads all the values