My impression, contrary to what I have read in this posting, is that on Fox and ABC, 720p is superior to 1080i for sporting events, since the signal is being broadcast at 60 frames/sec v 30 with the 1080i signal-hence,
Not necessarily. Back when HDTV was first starting to become popular, 720p was superior to 1080i for sports. But now, cameras and transmission technology have made 1080i look the same if not better than 720p. Yes, 720p does give you double the framerate, but again, that doesn't necessarily mean you are getting a "better" picture.
that is why I want to find out how to set my cable box to output both resolutions to the tv.
We would need to know what kind of cable box you have to help you out. But normally, you turn the cable box off, press the menu button on the box itself, and there should be a page to let you select resolutions. If you want the native resolution sent to your tv, select 480p, 720p, and 1080i. If you just want 1080i to be sent all the time, only select 1080i.
watching the playoff game today on Fox, it appeared to have more depth and slightly sharper when I set the box to 720 v 1080.
That all depends on how the cable box scales the picture, and how your tv scales the picture. I have one older tv that works much better with the cable box set to output only 1080i. And I have a newer tv that looks much better when the cable box outputs both 720p and 1080i.