But the more broadly heard message is negative: Nearly half of the girls say Mr. Trump’s comments about women have affected the way they think about their bodies.

The data, analyzed by David Rothschild and Tobias Konitzer of PredictWise and based on a poll of 332 girls, shows a generation of girls raised to believe that women can do anything men can do yet aware that they have not yet. Forty-four percent would definitely or most likely vote for Mrs. Clinton if they were old enough to vote, and 15 percent for Mr. Trump.

The campaign as a whole has inspired almost equal parts ambition and wariness about running for office. Twenty-two percent said Mrs. Clinton’s candidacy had made them more likely to want a leadership position in their careers, while 17 percent said it had made them less likely to want to be a leader. Fifteen percent said Mr. Trump’s candidacy had made them more likely to want a leadership position; 27 percent said the opposite.