And if you don't believe me, here's something that you could try (with an instructor on board, obviously). In level cruise, at a safe height (and 2000' seems very low to me), pull the mixture all the way back. Engine will stop producing power and windmill. Trim for best glide. Push mixture all the way in again. Engine will work again. Simple.
Preferably in the overhead of your home field! Always expect the worst.
And 2000 feet should be more than ample - you should be able to glide it in from 1000' anywhere in the circuit. Except at Elstree, when you may be quicker going to Denham, or Panshanger.
SD