I put a 35" tire under my 2004 ranger and it fit between the frame rails... barely. I have not measured but I would have to believe that the F150 frame is significantly wider than the rangers. Get a 35" spare and test it. Worst case scenario is you have to fab (or have fabbed up if you don't have a welder) a spare holder of some kind. You can get very creative.

 

It works. I went mud riding and all kinds of stuff with it back there, and it never came loose. Just make the bungee cords as tight as you can get them. You can tie a knot in them to shorten them a little to get them tight