Ah-HAH. (O, a-JA) "Estadounidense" puede ser un nombre
I had trouble with some of the exercises because I believed that 'estadounidense' was only an adjective. (See https://www.duolingo.com/comment/517903, which is a loooooong discussion following the lesson sentence "I am an American".) So, if the question said, "He is an American author," then I thought it was fine to say, "Él es un autor estadounidense." But I didn't realize it could be used as an alternative for "He is an American," as well.
As a lifelong resident in and citizen of the United States, I deeply dislike the cultural imperialism that blithely claims a name which should mean two continents for a single nation - but in English, there is very little in the way of an accepted alternative. (I personally have started saying 'USian', but that's partly because it looks funny, so it has the advantage of not only saying what I mean but also making people blink and think for a second about what I am doing.) And so I was pleased to find 'estadounidense' as a term that was, in fact, according to many native speakers, preferable to 'americano/a' in many Latin American contexts. So I'm doubly pleased to find, per WordReference.com, that it can be a noun.
I realize not everyone finds this problematic, and I'm not interested in a political debate about whether the use of 'American' to mean 'someone from the United States of America' should or should not offend, or whether the fact that Mexico is officially Estados Unidos Mexicanos should affect the decision. It bothers me, and that's all I really need to know.
So for everyone who has gotten snarled in that discussion or others, who like me failed to grasp that the noun was an option - it is!
Soy una estadounidense contenta. :)