(CNN) - A new poll is offering more evidence that the battle for Wisconsin and its 10 electoral votes is up in the air.
According to a new Marquette Law School survey released Wednesday, 49% of likely voters in the Badger State say they'll vote for President Barack Obama, with 46% backing Republican challenger Mitt Romney. The survey's three point edge for Obama is within the poll's sampling error.
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The survey was conducted August 16-19, entirely after Romney announced House Budget Chairman Paul Ryan as his running mate on the GOP ticket. Ryan is a seven-term congressman from Wisconsin. In Marquette's previous poll, conducted in early August before the Ryan announcement, Obama held a 50%-45% advantage.
"The two-point shift in Romney's direction is within the margin of error for the poll but suggests Ryan's addition to the ticket may have slightly increased Romney's chances in Wisconsin," said Professor Charles Franklin, director of the Marquette Law School Poll.
According to a CNN/ORC International survey, which was released last week and which was also conducted entirely after Romney added Ryan to the GOP ticket, Obama held a 49%-45% advantage over Romney. The president's four point margin over the presumptive Republican presidential nominee was within the survey's sampling error.
Last Thursday CNN turned Wisconsin from "lean Obama" to true "toss up" on its electoral map.
Obama won Wisconsin by 14 points over Sen. John McCain in the 2008 presidential election.
In the race to succeed retiring four-term Democratic Sen. Herb Kohl, the poll indicates the Republicans currently have the edge. According to the survey, former Gov. Tommy Thompson holds a 50%-41% lead over Democratic Rep. Tammy Baldwin. Thompson won the state's August 14 GOP Senate primary.
The Marquette Law School poll questioned 706 registered voters, including 576 likely voters, by telephone. The survey's overall sampling error is plus or minus 3.8 percentage points, with a sampling error of plus or minus 4.2 percentage points for likely voters.