Obvious from the numbers?
It's great to hear people thinking about new safety angles. When I first learnt to drive and after my first prang, my daddy told me the best way to avoid an accident was planning how not to be there at the time. It worked for me.
Proving the jump seat occupied hypothesis would be a lot of work however and besides it's possible the NTSB have already thought about this angle. I expect you realise already that proving correlation is not the same as proving causation. Skewed data integrity will certainly be a problem too. Accident reports record detailed information about jump seat occupancy but equally detailed information for the remaining comparable population of uneventful flights will be difficult to recover.
Then you have to demonstrate that correlation was not influenced by other factors. Jump seat occupancy (especially before 9/11) could have been influenced by whether the aircraft was fully occupied. It may be (although I do not know) that fully loaded aircraft are more likely to have serious accidents. That might bias the result towards an occupied jump seat.
There's other steps too but finally you still have to demonstrate that there was an insignificant probability that it was all just chance. Not easy with a small sample of positive data. History has plenty of examples of things that looked likely or even obvious that turned out later to be just not correct. Two easy to read (non-mathematical) books for anyone interested in the conflict between human nature and scientific data are:
The Tiger That Isn't by Michael Blastland and Andrew Dilnot,
and Bad Science by Ben Goldacre.
Finally a cautionary tale about the obvious from my younger days: We had bet the company on a new product but 3 out of 4 of the first models we built were under performing. I'd been away and when I returned every engineer was working to find what was wrong with the 'defective' models. It was Christmas week and we were facing the prospect of not being with our families on Christmas day. I knew my engineers were capable guys who would be doing the right things so something else had to be wrong. I took a walk to feed the birds in the park out back. That's when I realised the asumption we had all made. I ran back and moved the guys onto analysing the 'good' models. Sure enough we had the answer within an hour. All the better performing 'good' models had been built with one incorrectly marked and therefore out of specification component (and it was overstressing several others). It was sobering to realise that we could have screwed Christmas and maybe even the Company's future (not to mention my own reputation) because we thought something was obvious without verifying it adequately.
Stay safe!
STAN