NEW YORK (AP) — ‘‘President Obama is a Muslim.’’ ‘‘He’s not an American citizen.’’ ‘‘He wasn’t even born here.’’

None of this is true. But to surprising levels, it is believed.

Blame it on the media, or on human nature. All presidents deal with image problems — that they’re too weak or too belligerent, too far left or far right. But Obama also faces questions over documented facts, in part because some people identify more with the rumormongers than the debunkers.

‘‘Trust and distrust — that explains almost all of it,’’ says Nicholas DiFonzo, professor of psychology at the Rochester Institute of Technology and an expert on rumor and gossip research. ‘‘We are in such a highly polarized political environment. Our country is sorting itself into more closely knit, opposing factions each year’’ — factions, DiFonzo suggests, that in turn become ‘‘echo chambers’’ for factoids that aren’t fact at all.

Nearly one in five people, or 18 percent, said they think Obama is Muslim, up from the 11 percent who said so in March 2009, according to a poll released Thursday. The proportion who correctly say he is a Christian is just 34 percent, down from 48 percent in March of last year.

The White House even felt compelled to respond with a terse knockdown from spokesman Bill Burton: ‘‘The president is obviously a Christian. He prays every day.’’

Obama is the Christian son of a Kenyan Muslim father and a Kansas mother. Born in Hawaii, he lived from ages 6 to 10 in predominantly Muslim Indonesia with his mother and Indonesian stepfather. His full name, Barack Hussein Obama, sounds Muslim to many.

Confusion about Obama’s religion was common, and sometimes encouraged, during the 2008 campaign. An Associated Press photograph that circulated on the Internet, and was posted on The Drudge Report, showed Obama dressed in traditional local garments — a white turban and a wraparound white robe — during a visit to Kenya in 2006. Democratic rival Hillary Rodham Clinton may have contributed through her response to a question, during a ‘‘60 Minutes’’ interview, about whether he was a Muslim. ‘‘There’s nothing to base that on,’’ she said. ‘‘As far as I know.’’

Others have helped keep rumors about Obama’s religion and birth alive. Conservative commentators including radio talk show host Michael Savage have repeated debunked claims that Obama attended a radical Muslim madrassa in Indonesia. Rush Limbaugh has facetiously referred to ‘‘Imam Obama’’ in recent days, and last year praised a woman who at a Delaware town hall meeting questioned Obama’s citizenship. Lou Dobbs gave significant air time to such ‘‘birther’’ claims on CNN — despite his own insistence that he believed Obama was born in the U.S.

The new survey, conducted by the nonpartisan Pew Research Center and its affiliated Pew Forum on Religion & Public Life, is based on interviews conducted before the controversy over whether Muslims should be permitted to construct a mosque near the World Trade Center site. Obama has said he believes Muslims have the right to build an Islamic center there, though he’s also said he won’t take a position on whether they should actually build it.

We have never been without misperceptions, but they are speeded and multiplied in the Internet age. Last month, right-wing bloggers — citing unnamed sources within the Laredo Police Department in Texas — reported that the Mexican drug cartel Zetas had captured two Laredo ranches. The story was picked up by author-pundit Michelle Malkin and other conservatives.

Inquiries from local media and the liberal Web site Talking Points Memo turned up different news: The raids never happened.

‘‘The Internet has made it worse,’’ says Lori Robertson, managing editor of the website FactCheck.org, a nonpartisan project run under the Annenberg Public Policy Center of the University of Pennsylvania. ‘‘Any of these rumors are more rampant, and there’s more stuff about them — blogs writing about conspiracy theories. People are exposed to it more.’’

Robertson says her organization has been asked hundreds of times about Obama’s religion, even after FactCheck published an explanatory article in early 2008 called ‘‘Sliming Obama.’’ It focused on the chain e-mail that many believe helped spread the lie.

Despite what the e-mail claimed, FactCheck.org has noted that Obama was sworn into office as a U.S. senator using the Bible instead of the Quran; a photograph was posted to prove it. FactCheck also posted videos of Obama reciting the Pledge of Allegiance in the Senate, in an attempt to counter claims that he refused.

Still, the questions about Obama’s faith didn’t stop.

‘‘Did Obama order creation of a postage stamp to honor a Muslim holiday?’’ FactCheck.org’s answer: ‘‘The first class stamp honoring Eid al-Fitr and Eid al-Adha was first issued eight years ago. Obama has followed Bush’s practice of reaching out to Muslims on Ramadan.’’

Superstitions and myths are timeless and universal, and so are the people who exploit them, whether Holocaust deniers, race supremacists or conspiracy theorists.

Misinformation in the mass media age was captured by the author-columnist Walter Lippman in his classic ‘‘Public Opinion,’’ published in 1922. Finding that world events were driven by a tiny minority manipulating the rest, Lippman noted ‘‘the comparatively meager time available in each day for paying attention to public affairs, the distortion arising because events have to be compressed into very short messages, the difficulty of making a small vocabulary express a complicated world.’’

The problem wasn’t only with the media, but with the public.

‘‘People, he wrote, ‘‘live in the same world, but think and feel in different ones.’’ Lippman believed many ‘‘suffer from anemia, from lack of appetite and curiosity for the human scene.’’

And so millions have thought that the country was overrun with communists, that John F. Kennedy was taking orders from the pope, that AIDS spreads through casual contact, that Saddam Hussein or even the George W. Bush administration helped plan the Sept. 11 attacks. In the 1990s, when the government was running a surplus under the Clinton administration, a poll showed substantial numbers of people thought it was running a deficit.

DiFonzo was stunned when he heard one of those rumors stated as fact in his upper-level social psychology class last year. A student raised her hand and insisted, ‘‘But George Bush was behind the bombings of Sept. 11.’’

‘‘She was serious,’’ DiFonzo said, adding that he believes she accepted the rumor because other people in her life gave her the impression that it was plausible.

‘‘This isn’t a partisan thing,’’ he said. ‘‘It’s not a characteristic of Democrats or of Republicans. It’s a human characteristic. It’s a place that we happen to be at in our culture today. What seems outlandish is often based on what we think may be plausible.’’