Among Republican voters, 31 percent agreed that medical marijuana would have a positive effect on society.
Younger voters, typically seen as more receptive to relaxing drug restrictions, were the least likely to agree on medical marijuana's positive effect.
Among participants between 18 and 25 years old, 58 percent disagreed with the survey's statement.
"The age breakdown was a little bit surprising," Utah Foundation research analyst Mallory Bateman said.
The survey included 22 participants between the ages of 18 and 25 years old, compared to 80 who were 61 to 70 years old, Bateman said.
Connor Boyack, president of Libertas Institute, said it is reasonable that older Utahns would support medical marijuana in larger numbers than their younger counterparts.
Many aging individuals have used marijuana themselves, or know friends and family who have, Boyack said, and as a group they experience the health concerns that can be relived by medicinal cannabis.
"Of course they want the ability to try it out," Boyack said. "They know that the propaganda they hear is pretty silly."
And individuals in both age groups were predominately Republican, Bateman said, with roughly half of each group identifying as Republican.
But Boyack said the survey asked an "irrelevant" question by focusing on societal impact rather than the impact for individual patients.
The discussion around legalization of medical marijuana deals with the sick and suffering, Boyack said, not the state as a whole.
"It's not a matter of aggregate impact, if that can even be quantified," he said. "It's a matter of doing the right thing for the people who are currently illegally, using this alternative treatment."
The survey was conducted during the 2016 legislative session as lawmakers debated two bills aimed at allowing limited access to medical cannabis for individuals with qualifying illnesses and conditions.
Both bills were approved by the Utah Senate, but stalled in the House as lawmakers juggled budget priorities and attempted to merge the competing marijuana proposals.
Lawmakers are expected to debate the issue again next year, and medical marijuana advocates have made overtures to a potential ballot initiative.
Boyack said the plurality support implied by the Utah Foundation poll is encouraging, despite the poll's weaknesses.
"With a flawed question," he said, "I think it's a pretty positive result."