Really. Clocks on upper floors of a building tick faster than those at the ground by 2.5x10-15 seconds for every 6 floors you go up thanks to the effects of General Relativity. Indeed, GPS satellite's clocks at orbital altitudes will tick faster by about 45,900 nanoseconds per day because they are in a weaker gravitational field than atomic clocks on Earth's surface.
So General Relativity predicts that clocks in a stronger gravitational field will tick at a slower rate. But Special Relativity predicts that stationary clocks will appear to tick faster than moving ones. Remarkably, these two effects cancel each other for clocks located at sea level anywhere on Earth.
If a hypothetical clock at Earth’s north or south pole is used as a reference, a clock at Earth’s equator would tick slower because of its relative speed due to Earth’s spin, but faster because of its greater distance from Earth’s center of mass due to the slightly bloated equator.
Clocks at any altitude above sea level do tick faster than clocks at sea level; and clocks on an airliner and the Space Shuttle do tick slower than stationary clocks,