Chi-square test of independence 1/5 Prof. Martinez has decided to undertake a careful analysis of her student evaluations from the past several years. Question 17 on the evaluation form is "Would you recommend this professor to another student?" A matter of special concern to Prof. Martinez is how she is viewed by students of different majors. Each of Prof. Martinez's students can be placed into a category according to the student's major school. (Students who have majors from more than one school are not included.) So, there are two variables under consideration: student's major school ("School of Social Sciences", "School of Engineering", or "School of Physical Sciences") and response to Question 17 ("No", "Maybe", or "Yes"). The contingency table below contains a summary of the responses to Question 17 for a random sample of 500 of Prof. Martinez's students. In each cell of the table is written three numbers: the first number is the observed cell frequency (f); the second number is the expected cell frequency (f) under the assumption that the variables student's major school and response to Question 17 are unrelated; and the third number is the following value. (fo-E) (Observed cell frequency-Expected cell frequency) 2 JE Expected cell frequency The numbers labeled "Total" are totals for observed frequency. Part 1 (fo-JE) Fill in the missing values in the contingency table. Round your expected frequencies to two or more decimal places, and round your three or more decimal places. values to JE Send data to Excel Student's major school School of Social Sciences School of School of Engineering Physical Total Sciences 44 20 41 "No" 26.25 105 1.488 45 21 37 "Maybe" 49.03 25.75 28.22 103 Response to Question 17 0.331 0.876 2.732 149 84 59 "Yes" 73.00 292 1.658 Total 238 125 137 500 Part 2 Answer the following to summarize the test of the hypothesis that the variables student's major school and response to Question 17 are unrelated. For your test, use the 0.05 level of significance. (a) Determine the type of test statistic to use. Type of test statistic: (Choose one) (b) Find the value of the test statistic. (Round to two or more decimal places.) (c) Find the critical value for a test at the 0.05 level of significance. (Round to two or more decimal places.) (d) Can Prof. Martinez conclude that the variables student's major school and response to Question 17 are related? Use the 0.05 level of significance. Yes No