The results reported here about this Brown Univeristy study have been known since at least the 1970s.  I think I read about them in the 1980s.  They make for an interesting case study in how hard it is to change some things.

“Starting times were shifted from 8 to 8:30. All class times were cut 5 to 10 minutes to avoid a longer school day that would interfere with after-school activities. Moss said improvements in student alertness made up for that lost instruction time.

The portion of students reporting at least eight hours of sleep on school nights jumped from about 16 percent to almost 55 percent. Reports of daytime sleepiness dropped substantially, from 49 percent to 20 percent.

First-period tardies fell by almost half, students reported feeling less depressed or irritated during the day, health center rest visits dropped substantially; and the number of hot breakfasts served more than doubled. Moss said the healthier breakfast probably aided classtime alertness….”

But it’s not impossible, since a few school districts have managed to make the switch.