Just throwing seed down is very ineffective and considering what seed
costs, a waste of
money. To do a 1/2 acre, I'd rent a slice seeder. It has discs that
cut a series of grooves
about 2" apart, and then drops seed from a hopper. That results in
excellent germination.

But, you should also consider what you have to start with, what the
soil composition is, etc.
For example, if you have hard compacted soil, then that needs to be
addressed. Or if the PH is
off, that should be fixed. Or if you have mostly crappy, coarse,
weed type grasses, then it
would be better to kill it all off and establish a new lawn with
qualtiy seed. Best time for that is
Fall. If you do it now, it's harder, more competition from weeds,
more water with increasing temps, etc