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