Should consumers be able to control how companies collect and use their personal data?

At a dinner honoring privacy advocates this week in Washington, Timothy D. Cook, the chief executive of Apple, gave a speech in which he endorsed this simple idea. Yet his argument leveled a direct challenge to the premise behind much of the Internet industry — the proposition that people blithely cede their digital bread crumbs to companies in exchange for free or reduced-priced services subsidized by advertising.

“You might like these so-called free services,” Mr. Cook said during the event held by EPIC, a nonprofit research center. “But we don’t think they’re worth having your email or your search history or now even your family photos data-mined and sold off for God knows what advertising purpose.”

Now a study from the Annenberg School for Communication at the University of Pennsylvania has come to a similar conclusion: Many Americans do not think the trade-off of their data for personalized services, giveaways or discounts is a fair deal either. The findings are likely to fuel the debate among tech executives and federal regulators over whether companies should give consumers more control over the information collected about them.

In the survey, which is scheduled to be made public on Friday, 55 percent of respondents disagreed or strongly disagreed that “it’s O.K. if a store where I shop uses information it has about me to create a picture of me that improves the services they provide for me.”