The results of that study are in the chart above (compiled by the Los Angeles Times from the CDC study). Note that African-American fathers are no different from White or Hispanic fathers in performing the duties of fatherhood, and in some cases do an even better job.
Of course this brings up the question -- why is this mistaken belief so prevalent in our society? The obvious answer is that we are still a long way from solving our problem with race in this country. Some progress has been made. In the 1960's, a few tools used by racists against African-Americans were eliminated with the passing of the Civil Rights laws.
Unfortunately, those tools of racism were replaced by an expanded effort at propaganda. Since the racists didn't have their cherished tools to keep minorities down, they used lies to attempt to accomplish the same purpose -- and sadly, some of those lies (like the myth of the absent African-American father) came to be accepted by many (some of whom were not racist, but just gullible).
I applaud the CDC for this study, and websites like Think Progress who are actively trying to destroy the racist propaganda. The Los Angeles Times is also to be credited for their coverage. Hopefully, this becomes widely known very soon -- and we can put this racist myth behind us.