Hello!
It was nice to get the letter from you!
Actually, i don't have sisters or brothers, but i understand you perfectly. You can go on trying to be a good example to your sister, but i'm not sure if it would make sense. Maybe you shouldn't tell your parents about your sister's behavior and just try to talk about it with her instead and she might improve her attitude. I think, it's annoying when your younger sister is driving you mad. If i had this problem, I would talk to her and if it wouldn't help, then i would talk to the parents and try to solve this problem using their advice.
Anyway, i hope to hear from you soon.
Bye-bye!