“It’s been largely an insider conversation up until now,” said William H. Guenther, CEO and founder of Mass Insight. “The good news is, consumers want more information. . . . So you’ve got a willing public. We just have to make it more transparent and easier for them to gain access.”

The survey found that 87 percent of respondents considered it important to have clear information about the cost of medical care ahead of time. But 82 percent said they did not have information allowing them to compare cost and quality before getting a medical procedure.

Three-quarters did not know about the price-transparency requirements in the 2012 law.

More than 90 percent agreed that quality of care is “more important than anything else — even price.” But 55 percent also said that cost was a factor when choosing where to go for care.

Barbara Anthony, the state undersecretary of consumer affairs and business regulation, said she was heartened by the results. “It’s exciting to me that people want this,” she said.

Anthony said many don’t know about the requirements in the new law because the biggest change is yet to come — when the insurers launch their price-comparison websites on Oct. 1. Currently patients can call to request the information, but few do.

Brian Rosman, director of research at the Boston-based consumer advocacy group Health Care for All, said the price information will be useful to people with high-deductible health plans, but he doubts it will do much to lower health care costs. “Patients have a right to know this, but this isn’t going to fix the system,” he said.

The poll found that among those surveyed who had had a medical procedure in the last year, more than half paid a co-pay of less than $100.

The survey was conducted for Mass Insight by Opinion Dynamics Corp. in partnership with the Associated Industries of Massachusetts, Harvard Pilgrim Health Care, the Massachusetts Hospital Association, and the Massachusetts Medical Society. Phone interviews were conducted with 450 residents from April 30 through May 4. The margin of error was 4.6 percentage points.

Some insurers, such as Aetna and UnitedHealthcare, have already developed websites that enable members to comparison-shop for services such as MRIs or lab tests. Those companies “have seen tremendous growth in terms of their members using it,” Anthony said. Others are making good progress on their websites, she said.

“What we’re trying to do is reset attitudes here,” Anthony said. “This is really going to be a revolution in terms of the consumers’ awareness of cost and quality information. Like all revolutions, it has to start somewhere. It should take several years.”