Smartphones - are they fully functionally tested?
Typically in large volume electronics trial production runs are performed first, and all produced units undergo functional testing. Once target failure rate is reached, all production parameters are freezed and mass production begins. It is usually safe to assume that mass production runs will have the same acceptable failure rate, so only a few units from mass-produced batches are tested, in order to confirm there's no sudden rise in defect rates. Most units are packaged as is, without anybody switching it on to confirm it really works.

Of course, that doesn't exclude end-of-line testing of individual components. Typically, once the main PCB is fully assembled and the software is flashed on it, devices like this one are connected to the test points and production tests are performed. This covers most of the defects and is much cheaper than a robot interacting with the finished product (imagine a robot capable of putting a SIM card in a phone).

Here's a paper published by Fujitsu which touches the subject of testing Android-based devices:


  ... operations on Android were essentially used at first in the testing process at the time of manufacturing. [...] This sometimes caused problems such as unexpected test operations and excessive testing times. To solve these problems we have changed the testing process so that basic smartphone operations are run in the kernel layer, and the effects of Android OS on testing can be eliminated.


Simply put, they have tried to use Android interface to perform end of line tests, but that didn't work out very well.