Is it possible to make python throw errors if the type of the argument passed to the annotated function doesn't match the one specified?

Type hints implement PEP 0484 which explicitly lists as a non-goal:

While the proposed typing module will contain some building blocks for runtime type checking -- in particular the get_type_hints() function -- third party packages would have to be developed to implement specific runtime type checking functionality, for example using decorators or metaclasses. Using type hints for performance optimizations is left as an exercise for the reader.

From this it seems to follow that the Python developers have no plan to add the functionality that you seek. The quote mentions decorators and that does seem the way to go. In concept it seems straightforward -- the decorator would use get_type_hints() on the function to be decorated and would iterate through the arguments, checking their types against any hints, either throwing an error if there is a clash or simply passing on the arguments to the function. This would be similar to pzelasko's answer but with the decorator using the hints to automatically handle the boiler-plate code. The simplest approach would be to simply vet the arguments, though you should also be able to make a decorator which would raise an error if the return type clashes with the hint. I don't yet have Python 3.5 and don't have the time to pursue it -- but it seems like a good learning exercise for someone who wants to learn about both decorators and type hints. Perhaps you can be one of the "third parties" the PEP alludes to.