4. A survey of 540 college students, of whom 280 are female and 260 are male, was conducted as part of the study on college expenditures. According to this survey, 160 female students and 122 male students have purchased at least one digital version textbook. (a) (5 points) Give a 99% condence interval for the difference between the female and male propor- tions of students who have purchased at least one digital version textbook. (b) (6 points) Using a 1% signicance level, would you be able to conclude that the proportion of female students who purchased at least one digital textbook is larger than that of male students who purchased at least one digital textbook? Why or why not? Show your work