In the Vietnam War draft lottery conducted in the USA in 1970, the lottery numbers 1 through 366 were supposedly randomly assigned to the days of the year. Individuals having the birthday receiving lottery number 1 were first in priority to be drafted, and so forth down to those having the birthday with lottery number 366, who were last in priority to be drafted. The results of the lottery are summarized in the table. Draft Lottery Number 1-183 184-366 Jan-Apr 45 76 Birth Month May-Aug 61 62 Sep-Dec 77 45 a) If you had been eligible for the draft in 1970, would you have preferred a birthday between January- April, May-August, or September-December? Why? b) If the draft lottery numbers were truly randomly assigned (i.e., if lottery number were independent of birth date number), what frequencies would you expect to find in the six cells? c) Use a chi-square to test the hypothesis that the lottery numbers were in fact randomly assigned.