So, the American side lost this battle: because of this I don't think that it showed whether the Americans would win the war: they lost the battle but not by much, so the final outcome was undecided.
Instead I think that it helped to answer "how the Americans would fight".
But I think that the best answer would be that it showed the Americans that they could win: that they had a good chance at winning. Sadly, this is not one of the options.
