In the sentence:
Would a Chinese person typically assume this is a goat or a sheep?
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People usually say 山羊 when they mean a goat.
--- I don't think so.
Goat or Sheep, just only depends on the context or the environment!
Actually, the scene of language is as follows:
When a sheep comes, what the brain of a Chinese-speaking people presents/thinks about is: "羊 is coming."
When a goat comes, what the brain of a Chinese-speaking people presents/thinks about is ALSO: "羊 is coming."
That is to say, when a concept about any sheep or goat or any sheep-like or goat-like or any Caprinae-form animal comes into the brain of a Chinese-speaking people, he or she always thinks about "羊" only, usually without differentiation like a English-speaking people does.
Only if the Chinese-speaking people is need to differentiate sheep or goat in his or her concept, he or she says “绵羊” or “山羊”.
Similarly, in the area which people mainly eat pork (the flesh of a pig or hog), they usually refer to the pork as a single word “肉”. If the word “肉” leads to some ambiguity, they could say “猪肉” for the pork and say “羊肉” for the mutton (or flesh of goat). Furthermore, in the area which people usually only eat mutton (the flesh of sheep), they could say “山羊肉” to indicate the flesh of goat.
You would meet a phrase “鸡鸭鱼肉”, these four words all indicate the flesh as food. Under this phrase,“鸡”means chicken, “鸭” means duck, “鱼” means fish, “肉” means pork mainly or means any flesh of a mammal such as beef, mutton.
Please NEVER forget this truth: The meaning of a word only should be presented from the context or the environment!
Additionally, similarly, when a English-speaking people says "a cousin", that could puzzle a Chinese-speaking listener, the latter wonders what the "a cousin" exactly indicates: a 堂兄 or 堂弟 or 表兄 or 表弟 or 堂姐 or 堂妹 or 表兄 or 表妹? The fact about this conflict is: the English-speaking people usually do not differentiate those consanguinities, but the Chinese-speaking people care for that.
I did a quick whip round of some of my Chinese friends (well, 6 who are online currently) and came to the conclusion it could work either way, and doesn't really matter.
One made an interesting point that they don't really point out the difference in Chinese, but that she notices Chinese people say 'sheep' a lot more than 'goat' in English, which I think is an interesting point.