Final answer:
The star closest to the north celestial pole is typically Polaris, the North Star, which acts as a pivot point around which the entire northern sky appears to rotate.
Step-by-step explanation:
The star in question 4 that lies closest to the north celestial pole on the celestial sphere is most likely going to be Polaris, the North Star.
This is because, currently, Polaris is situated very near the north celestial pole and serves as a pivot point around which the entire sky appears to rotate due to Earth's rotation. Observers in the Northern Hemisphere can locate Polaris by finding the Big Dipper and drawing a line between the stars at the end of the 'bowl' of the Big Dipper, extending this line outwards to the next bright star, which is Polaris.
The opposite constellation, Cassiopeia, also rotates around Polaris, so if one constellation is not visible, the other can be used to find the North Star.