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2. [-/12 Points] DETAILS ILLOWSKYINTROSTAT1 11.HW.077. MIT NOTES UCLA conducted a survey of more than 263,000 college freshmen from 385 colleges in fall 2005. The results of students' expected majors by gender were reported in The Chronicle of Higher Education (2/2/2006). Suppose a survey of 5,000 graduating females and 5,000 graduating males was done as a follow-up last year to determine what their actual majors were. The results for females are shown in the table below. The second column in the table does not add to 100% because of rounding. Conduct a goodness-of-fit test to determine if the actual college majors of graduating females fit the distribution of their expected majors. (Use a significance level of 0.05.) Major Women - Expected Major Women - Actual Major Art & Humanities 14.0% 670 Biological Sciences 8.4% 410 Business 13.1% 685 Education 13.0% 650 Engineering 2.6% 145 Physical Sciences 2.6% 125 Professional 18.9% 975 Social Sciences 13.0% 605 Technical 0.4% 15 Other 5.8% 300 Undecided 8.0% 420 + Part (a) Part (b) State the alternative hypothesis. O The actual college majors of graduating females and their expected majors are dependent events. The actual college majors of graduating females and their expected majors are independent events. The actual college majors of graduating females fit the distribution of their expected majors. The distributions of the actual college majors of graduating females and their expected majors are not the same. The actual college majors of graduating females do not fit the distribution of their expected majors