Suppose the local state university wants to determine whether there is a relationship between a student's gender and a student's major in college. The registrar was asked to randomly select 55 students and record their gender and major. The majors were grouped into categories of Natural Science (NS), Social Sciences (SS), and Humanities (H). Answer the following questions based on the results in the table below. NS SS H Total Men 11 9 3 23 Women 9 13 10 32 Total 20 22 13 55 Part 1: 1. Determine the expected frequency for each of the cells within the table. 2. Compute the sample chi-square statistic from the contingency table. Conduct a chi-square test of independence to determine whether there is a relationship between gender and college majors. Show all of your work to support your chi-square test. 4. What conclusion can be determined from the results of the chi-square test? Part II: Suppose we are only interested in the college majors of the women in our study. We would like to compare our sample to the national percentage of women majoring in each of the categories (NS, SS, and H) and determine whether the sample distribution fits the national distribution. Suppose the national percentage of women majoring in Natural Sciences is 22%, majoring in Social Sciences is 28%, and majoring in the Humanities is 30%. NS SS H Total Women 9 13 10 32 1 . Conduct a chi-square goodness-of-fit test to determine whether our sample data fits the national distribution. Show all of your work to support your chi-square test. Version 2 August 2020 2. What conclusion can be determined from the results of the chi-square test