I'd stick that spare tire back on - it's only 50 pounds on a vehicle designed to handle between 10,000 and 13,000. I seriously doubt it's going to notice the spare tire. You're going to care a lot more about not having one if you get a flat than you're going to care about the very small fuel economy savings.
Also if your mom needs proof that an old F-150 isn't safe just because it's large... this is the 1997-2004 F-150 being crash tested at IIHS. It faired extremely poorly. I know, it's two years newer than yours. Compare that to the 2004 model that's 10 years newer in the next video.
http://www.youtube.com/user/iihs#p/u/1/6Wb66PzljP8
Here's the newer 2004-2008 model being crash tested - the engine compartment is destroyed, but the dummy 'lives'.
http://www.youtube.com/user/iihs#p/u/1/jongDRViwno
Question - what's the code to embed the videos directly in the post?