A clear majority of Americans still suspect there was a conspiracy behind President John F. Kennedy’s assassination, but the percentage who believe accused shooter Lee Harvey Oswald acted alone is at its highest level since the mid-1960s, according to an Associated Press-GfK poll.

According to the AP-GfK survey, conducted in mid-April, 59 percent of Americans think multiple people were involved in a conspiracy to kill the president, while 24 percent think Oswald acted alone, and 16 percent are unsure. A 2003 Gallup poll found that 75 percent of Americans felt there was a conspiracy.

As the 50th anniversary of Kennedy’s death approaches, the number of Americans who believe Oswald acted alone is at its highest since the period three years after the Nov. 22, 1963, assassination, when 36 percent said one man was responsible.

President Lyndon B. Johnson appointed the Warren Commission on Nov. 29, 1963, to investigate both Kennedy’s assassination and the killing of Oswald days later. The commission concluded that Oswald was the lone gunman.

Those who were adults in 1963 were almost as likely as younger Americans to say that Kennedy’s killing was a conspiracy involving multiple people — 55 percent, compared to 61 percent.

The Associated Press-GfK Poll was conducted April 11-15, 2013, by GfK Roper Public Affairs and Corporate Communications.  It involved landline and cellphone interviews with 1,004 adults nationwide. Results for the full sample have a margin of sampling error of plus or minus 3.9 percentage points; it is larger for subgroups.