Some of the budgie eggs were definitely fertilized. They were mating many times before the eggs were even laid. More importantly, there were dead chicks pushed out of the nest. On some other occasions, the hen just pushed the eggs out. I checked the broken eggs, and there were dead chicks inside too. Whatever caused the problem was either their inexperience, or external facts such as weather and/or the noises. One batch of eggs were pushed out of the nest during New Year's Eve. No thanks to the firecrackers...
Anyway, I can no longer try it any more. The male budgie just escaped a week ago. The hen won't be able to get any chicks without a male friend.