3.) [5 marks] Carry out a GoodnessofFit test comparing these sample proportions to the prOportions expected in the wild. Determine the Xg-score for the sample, and then use cal culus (via the procedure outlined in part 2) to determine the threshold size of X2score that would be used to determine whether this sample was showing statistically signicant differ ences from the expected (wild) pOpulation pr0portions of personality types. When carrying out Newton's method, start from a guess of m0 = 6, carry out one iteration, and keep the rst four places after the decimal. Does this sample achieve statistical signicance? Your writeup for Part 3 should include most / all of: 0 Determining the value of 3(ng for this data set. 0 Determining the appropriate values for k, v, and I'(v/2) (again using software to eval uate the Gamma function). 0 Simplifying the probability distribution function p(m,v) based on the values of k, v, and Us / 2). 0 Determining the integral of p(:n, v) with respect to a: to allow use of Newton's Method. 0 Use of Newton's Method to get a precise estimate for Xeject. o A discussion of whether ngs is above or below Xfeject, and what this suggests about the proportions of personalities observed in the group of guppies raised in safety