What would be the O-notation for adding a word into an alphabetically sorted linked list?

what would be the O-notation for adding a word into an alphabetically sorted linked list?

What would be the O-notation for adding a word into an alphabetically sorted linked list?
I would say that it would be O(n) unless the list was also a binary tree which would be more efficient. The insertion even if the list is sorted would possibly have to look at every element in order to determine the insertion position.