I recently poured a 12x20 concrete slab for a patio with a "broom" finish. I would like to know if a "knock-down "finish can be added to it now that it has cured about a week. If it can, what is the proper concrete mix and the step-by-step procedure?

 

It can be done. You could use a variety of better products, but the easiest for a DIYer to obtain will come from Lowes, HD, etc. Here are the steps:
1) THOROUGHLY clean the slab of all sealer, paint, dirt, oil, etc. If you used a curing compound on the slab, it will need to be completely stripped.
2) Mask off any walls, doorframes, etc.
3) Mix 2 parts play sand or white sand to 1 part portland cement. Dry mix it first in a pail. Then add acrylic concrete fortifier or concrete bonding agent. Quikrete sells both at the stores I mentioned. You can use a little water too to get it to a consistency like a very heavy paint or pancake batter.
4) get the floor damp but with no standing water, and use a whitewash brush to drip or splatter the mixture on the slab. Either immediately or waiting a minute or two, use a steel concrete trowel (not a float or a bricklayers triangular trowel) to skip over the surface. It "knocks down" the high spots or blobs and flattens them down closer to the concrete surface. You don't want to completely flatten or eliminate them, just knock 'em down and spread them out a little. The amount will depend on how it looks to you.
5) allow it to dry for a day or so before walking on it.

Be aware that the splatter coat will almost certainly be a different color than your existing concrete. Usually it is darker than the existing. If you don't like the multicolored look, you'll have to paint or stain the floor afterwards. Good luck.

 

Sorry, I was reading this as a patio room (indoors). The same thing would apply outdoors, but it should be sealed after completion to protect it from the elements.