Test the Hypothesis Yourself
Take a carton of eggs and try balancing the eggs on end today. Can you stand any of them up (without resorting to tricks like putting salt under the eggs)? Can you stand eggs on their small ends as well as their large ends? Keep track of your results and repeat the process on the equinox. Do you note any differences? A simple hypothesis to test is: Eggs can only be balanced on-end on the equinox. If you can balance an egg any other day, you've disproven the hypothesis. It's that easy!
One thing I find neat about egg-balancing is that a balanced egg will hold its position until a vibration knocks it down. How long can you keep an egg standing?