In an article published in Psychology of Music (2010), researchers reported the results of a study conducted to investigate the effects of "romantic lyrics on compliance with a courtship request." The researchers recruited undergraduate female students who were studying social and managerial science and told them that "the purpose of the study was to discuss organic products with another participant." When a participant came in for the study, she was randomly assigned to listen to either a romantic song or a neutral song. After three minutes, she was greeted by a male "confederate" (chosen and trained by the researchers to pretend to be another participant), who while discussing the organic products also asked for her phone number so that he could call her up to ask her out.

The male confederate was kept unaware of the aim of the study and was trained to use the same script when talking to all the females.

Of the 44 women who listened to the romantic song, 23 gave their phone numbers, whereas of the 43 who listened to the neutral song, only 12 did.

Find the observed difference in the conditional proportion of females who gave their phone number to the male confederate between those who listened to the romantic song and those who listened to the neutral song.Round to three decimal places.