Question

To an observer in New York State, stars appear to rise in the

Answer 1

2) south






The observers are on the opposite side of the sun, so they are seeing stars that were previously obscured by the sun's light.
Explanation:
Objects in space are constantly moving. The moon is orbiting the Earth, which in turn is orbiting the sun, which is orbiting the center of the Milky Way galaxy. As such, our perspective of the universe is always changing.
At any given time we can see about half of the sky. The Earth blocks the other half. As the Earth rotates, however, that view of the sky changes. For someone standing on the equator, one full rotation of the Earth will show the entire celestial sphere. For someone standing on the north pole, however, the visible portion of the sky will only appear to rotate. New York is somewhere in between, so the south part of the sky will change and the north part will always be visible.