This question might be better suited to the Physics StackExchange, but the back-of-the-envelope calculation goes like this:
The Earth's magnetic field is 31.869 µT, and a refrigerator magnet is 5000µT. So the refrigerator magnet will very readily affect the magnetometer (not usually called a hall-effect sensor) on a smartphone.
However, you will run into two very serious problems
The strength of a magnet follows the inverse square law -- it drops off rapidly with distance. You can verify this with a handheld compass: see how close your magnet needs to be in order for it to pull the needle away from magnetic north.
The magnetic field curves around the magnet. For the earth, this is not a major concern because you are (more or less) standing on the surface where the lines run (more or less) straight from north to south.
For your room-sized magnetic field to work, you would need to establish a magnet far enough away that its field lines would have minimal curvature through the area that you want to measure, and strong enough that those field lines would have enough strength to dominate the 31.869 µT provided by Earth's magnetic field.