Answer :
The observation that best supports the claim that guarding the nest increases the chances of the female long-tailed sun skink's eggs hatching is:
1. Fewer eggs are eaten when females keep egg-eating snakes away from the eggs in their nests.
This observation directly connects the act of guarding the nest with a positive outcome, which is the protection of the eggs from predators like egg-eating snakes. By keeping these predators away, the female skink increases the likelihood that more eggs will survive and hatch successfully. This behavior enhances the reproductive success of the female skink by safeguarding her offspring.