"Nein, ein anderes."
You have to keep in mind though, that not all languages follow English rules in grammar or syntax. "No, a different" is correct in a LITERAL translation, but literal translations can sometimes be of little use when you're trying to desipher what the speaker/text is really trying to put across. Just translate all the previous german sentences in this course word for word and you'll realise most don't make sense when translated literally.
It is correct English, actually. An other isn't contracted but it's often a more precise or formal way of distinguishing difference than saying "another": instead of gesturing sequentially, it shows genuine "otherness." Theoretical discussions often refer to "an other" for that reason.