Prof. Harris, always interested in improving her teaching effectiveness, has decided to undertake a careful analysis of her evaluations from the past three years. A matter of special concern to her is how she is viewed by students of different majors. She's decided to look at the last question on the teacher evaluation form, Question 17, which is, "Would you recommend this professor to another student?" Each of Prof. Harris' students can be placed into one of three categories according to the student's major school, as shown in the contingency table below. (Students who have majors from more than one school are not included.) This table contains a summary of the data that Prof. Harris has collected for 500 of her students. Each of the 500 students is classified according to two variables: major school ("School of Social Science", "School of Engineering", or "School of Physical Sciences") and response to Question 17 ("No", "Maybe", or "Yes"). In the cells of the table are written the respective observed frequencies. In addition, three of the cells have blanks beneath the observed frequencies. Fill in these blanks with the frequencies expected if the two variables, response to Question 17 and student's major school, are independent. Round your answers to two or more decimal places. Send data to Excel Student's major school X 5 2 School of Social School of School of Physical Total Sciences Engineering Sciences 42 32 24 "No" 98 0 0 "Maybe" 43 32 29 104 Response to Question 17 153 68 77 "Yes" 298 0 Total 238 132 130 500