On the other hand, if the spaceship traveled at .3c instead of the .2c of the previous example, from Earth's frame of reference the trip would take 4666.7 light years (by the same reckoning as above, a signal sent out from the spaceship upon arriving would reach the Earth 6066.7 years after the spaceship left). But now the Lorentz factor would have gamma be 1.04828, so the duration of the trip from the frame of reference of the astronauts on the ship would be 4451.72 years, correct?

I'm just trying to get a feel for how the Lorentz Transformation affects how an astronaut perceived time as her/his spaceship traveled at speeds close to the speed of light.