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Over the past two years more companies are turning to high deductible health insurance plans. As of 2016, a quarter of all companies that offer health insurance made high-deductible plans the only choice, up from 13 percent in 2012, according to Consumer Reports. High-deductible plans are also the norm on the Affordable Care Act exchanges.

Lawmakers have pushed the plans as a way to cut costs by getting people to take control of the money they spend through health savings accounts. However, a recent Bucknell Institute for Public Policy poll shows many people aren't shopping around at all.

Amy Wolaver, the economist at Bucknell who directed the poll, says only about 28 percent of Americans are shopping for better prices.

"So the takeaway of the study is that it's very difficult to shop around for prices in health care," Wolaver said. "Very few people try, and of those who do try, they have difficulty in finding information."

Those headed to the hospital were the least likely to shop around, but even for those in need of outpatient care, just under 36 percent compared costs.

Lower-income and less educated families were less likely to compare prices than higher income, more-educated ones.

Ethnicity also factored in. African-Americans were the least likely group to seek prices, at 20 percent.

Wolaver says of those who did price shop, about one in four were actually able to get quotes from all the health care providers they asked.

While some states have made rules to make it easier for people to get prices, Wolaver says the lack of clear pricing poses challenges for those who hope to take control of their health care spending.

Another aspect to health care shopping that this poll didn't focus on, but which Wolaver wants to examine, is how many people are pushing their doctors for lower-cost alternatives. "I think the idea is that, if you're facing a high deductible, you might question your doctor more about, is this really necessary? Are there less intensive interventions that could also be successful?"

Click here to view the full results of the poll.