Well, in the process of manufacturing tin (Aluminum), foil, weak spots could allow the scanning rays through, so I wouldn't trust my brain to a simple tin foil hat. There can even be microscopic pin holes depending on the thickness...
In fact, beta radiation is used to measure the thickness of Aluminum foil, so it proves that the foil can only protect you so much (see below).
I'd much rather have a full j-channel interlocking body armor, preferably with chainmail underneath, as the interlocking round rings in the chainmail create an array of circular magnetic fields which can protect me from any rays that may get through the openings between the armor plates! And of course, the complete protection from outside of Diamond Plate Aluminum. For extra measure you can line the interior walls with foil, just to ward off any trace elemental radiation that makes it through somehow, such as through ventilation channels.From Wikipedia; http://en.wikipedia.org/wiki/Aluminium_foil
Aluminium foil is produced by rolling sheet ingots cast from molten billet aluminium, then re-rolling on sheet and foil rolling mills to the desired thickness, or by continuously casting and cold rolling. To maintain a constant thickness in aluminium foil production, beta radiation is passed through the foil to a sensor on the other side. If the intensity becomes too high, then the rollers adjust, increasing the thickness. If the intensities become too low and the foil has become too thick, the rollers apply more pressure, causing the foil to be made thinner.
By the way, here's my house!!