AITAH for standing up for my sister after my mom accused her of vaping?

I (19f) have a younger sister (15f). Well 1 day my sister went out with her friends and she went to this bakery. There was an uncleaned table that was empty and on top of that was an empty box that was meant for a vape. My sister took the box and put it in her pocket to throw it in the trash bin after she eats. Well unfortunately for my sister she forgot to throw it.

Afterwards when she came back home and the box fell out of her pocket then my mom yelled at her for having it, which i completely understand but when my sister told her story but my mom kept yelling at her so my sister tried to make my mom believe her but my mom took the box and said “I will tell your dad about how stupid you are with your stupid friends-“ and so I decided to cut my mom off and told her some good reasons why my sister couldn’t possibly vape (1- she is 15 and you have to be 18+ to even buy 1)

(2- even if she bought it somehow, where was the vape?) and etc.

My mom just called me some words and to be honest, I only defended my sister for 2 reasons: 1- my sister didn’t vape 2- I hate loud noises they always stress me out. (I tried to end the argument as soon as possible)

So am I the asshole?