The precinct level returns in Hinds County bolster the theory that a surge in black, Democratic turnout allowed Senator Thad Cochran to defeat Chris McDaniel, a Tea Party-backed state senator, in last month’s Republican primary runoff in Mississippi.
Mr. Cochran won by 6,693 votes. More than half — a net 3,532 votes — came from the most Democratic precincts in Jackson’s Hinds County, where President Obama won a combined 97.8 percent of the vote in 2012, according to figures released Tuesday night by the Mississippi secretary of state.