At a local college, an admissions officer surveys the incoming class of 1,000 first-year students concerning their preference of major. The officer randomly selects 100 of them and asks if they intend to major in liberal arts. Of the 100 first-year students, 62 state they intend on majoring in liberal arts. Assuming the conditions for inference have been met, what is the 95% confidence interval for the true proportion of first-year students who intend on majoring in liberal arts?