A new poll shows colleges could risk losing as much as a third of incoming students if classes remain entirely online in the fall.

Inside Higher Ed highlighted a survey of 2,800 high school seniors conducted by Carnegie Dartlet this month that shows the decision on how colleges handle classes in the fall will have a big impact on whether students will enroll.

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Roughly a third of respondents told the pollster they would defer or cancel an admission at a college that only offers classes online, while the vast majority expect a tuition discount for classes that aren’t in-person.

Inside Higher Ed reports:

The vast majority of high school seniors (95 percent) said a move to online coursework, even partially, requires at least some change to the cost of attendance.

Respondents reacted to scenarios of a college going online for part of the fall semester or going online for the entirety of fall. About a third said they expected a slight reduction in cost, a third would seek a significant reduction in cost and a quarter were satisfied with simply waiving campus fees associated with living on campus.

The poll comes as colleges across the country are announcing plans for the fall, with many vowing to reopen campuses, and others already set to remain largely online.

The University of Notre Dame announced this week it would resume classes on Aug. 10, two weeks earlier than normal, and skip the Thanksgiving break to reduce the chances of students bringing the virus back to campus.

The University of South Carolina announced similar plans to reopen in August and skip a fall break. Officials there then plan to transition to online classes after Thanksgiving. The University of Texas at Austin, Brown University, Purdue University and others also plan to re-open to in-person classes, The New York Times reports.

Officials at the University of California system, meanwhile, are preparing for mostly online classes in the fall, according to Inside Higher Ed.

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Terry W. Hartle, senior vice president of the American Council on Education, told the Times colleges are considering a variety of cleaning, testing, contract tracing and social distancing measures in hopes of managing spread of the disease to open schools this fall, but the biggest factor will be how the coronavirus spreads over the summer.

“Three months from now, who knows what we’ll be talking about,” he said.

Paul Browne, spokesman for Notre Dame, told the Times the university’s reopening plans center on conducting enough testing to detect and isolate students with the coronavirus, and officials there are consulting with top health officials to take precautions.

Professors are also preparing for both in-person and online classes, he said, in case things take a turn for the worse.

“If there were another outbreak, all of this is subject to change,” Browne said. “At this point, we’re confident, but we remain flexible.”