2. [8 marks] Suppose that a poll is conducted to ask university students who live on-campus "Do you have unprotected sex?". To encourage honesty, the instructions say If the last digit of your student number is 1, 4 or 7, you should simply say Yes. Otherwise, you should truthfully answer Yes or No. Note that the organization conducting the surveys does not have access to anyone's room number. (a) [5 marks] Suppose that everyone answers according to the directions, with 11,365 people responding No and 7,635 people responding Yes. Determine with justification the percentage of the students who have unprotected sex. (b) [1 marks] In addition to assuming that participants respond with the truthfulness described in the instructions, what other assumption is made in determining the percentage in (a)? (c) [2 marks] Suppose that the first bullet is modified to say "If the first digit of your room number is 1, 2 or 4, you should simply Yes to the question". Suppose that this Modified Poll is given, and the percentage of students who have unprotected sex is calculated. Would you trust the percentage obtained from this Modified Poll more or less than the percentage obtained in (a)