As we note in our new report on Donald Trump’s embrace of conspiracy theorists, “poll after poll shows that Trump supporters disproportionately subscribe to shocking conspiracy theories,” such as the false claim that thousands of Muslim-Americans in New Jersey celebrated on 9/11 or that climate science is a hoax.

A new survey released by Public Policy Polling today finds that respondents who have a favorable opinion of Trump are much more likely to believe in the conspiracy theories Trump promotes, including the discredited claims that President Obama is a foreign-born Muslim, that Justice Antonin Scalia died under suspicious circumstances and that vaccines are linked to autism.

One claim promoted by Trump, that Ted Cruz’s father was involved in the assassination of John F. Kennedy, didn’t appear to entirely convince his followers. But it did raise misgivings: while 7 percent of Trump’s fans thought Rafael Cruz was implicated in the assassination, 38 percent couldn’t say for sure one way or the other.

That’s not so bad for Trump, since simply muddying the waters was his main objective all along.