"a small hospital"
I think that big and small have both either forms "i" and "na" and they mean just the same. So, as far as I now: 大きい = 大き(な) 小さい = 小さ(な)
I thought 大きい and 小さい were い adjectives as opposed to な adjectives, and ,therefore, didn't need the な to be placed before a noun and qualify it. So what happens here?
There are a couple adjectives that can take both forms. In this instance, they're being used as な adjectives. Duo doesn't specify why, but maybe its just to introduce us to the concept that these particular ones can flip flop. I think it should still accept the い form and say "you can also say it like..." with the な form.