Assume that, at the University of Ottawa, Management and Engineering graduate students must take a similar statistics course during their studies. The university would like to assess the association between the placement of students in the Management and Engineering faculties and their final grade in the course. For this purpose, the university has categorized students' grades in the past five years into six groups of 90-100, 80-90, 70-80, 60-70, 50-60, and less than 50. The table below summarizes the distribution of the grades by faculty. Please note that the values in the table correspond to the number of students in each category. Grade 90-100 80-90 70-80 60-70 50-60 Less than 50 Faculty Management 30 35 20 10 5 7 Engineering 45 50 50 40 20 8 a) Are the required conditions for a chi-square test of homogeneity (independence) satisfied? Explain your answer. Answer the following two questions regardless of your answer to part a). b) Create a table with the corresponding expected counts and having row totals, column totals, and grand total. Round each cell value to two decimal places. Show your computation of the expected count for the number of students with a grade between 90 and 100 in Management. c) Perform a chi-square test to assess the association (or independence) between faculty placement and final grade at the 5% level of significance. Show your computation of the contribution to the chi-square statistic of the cell associated with the number of students with a grade between 90 and 100 in Management. Make sure you follow all the steps for hypothesis testing indicated in the Instructions section, explain each step, and confirm your results using statistical software