Assuming there was a 0.545% chance for visitors to start a conversation, and the chance didn't actually change between the tests.
In that case you'd have an ~8% chance to get 34 conversations or less for 8004 visitors, and also an ~8% chance to get 45 conversations or more for 6622 visitors, and there would be just a ~0.66% chance you'd actually see a gap that large (or more accurately: gap between any x<=34 and x=>45) by random chance, suggesting there was probably some change in p in between the tests.
Mind I just played with a specific p of 0.545% here, and also halfassed it.
Assuming there was a 0.545% chance for visitors to start a conversation, and the chance didn't actually change between the tests.
In that case you'd have an ~8% chance to get 34 conversations or less for 8004 visitors, and also an ~8% chance to get 45 conversations or more for 6622 visitors, and there would be just a ~0.66% chance you'd actually see a gap that large (or more accurately: gap between any x<=34 and x=>45) by random chance, suggesting there was probably some change in p in between the tests.
Mind I just played with a specific p of 0.545% here, and also halfassed it.