MGTS312_Samt2-akey_W2024

1 MGTS 312, Advanced Business Statistics W2024 Sample Midterm 2 Answer Key, Full Marks 30 Time: 50 minutes, Instructor: Dr. S. Ghosh [Note: While the actual midterm two will be of a similar format and contain the same number of questions, the questions from this sample midterm two will not be repeated. Moreover, just because there are no questions from a topic in this sample exam, it does not mean there will be no questions from that topic in the actual exam.] Closed book, closed notes, only aids permitted are a calculator, a formula sheet, and probability tables. Circle your MC questions with a blue or black pen on page 2 of this exam booklet. Name (PRINT) Student Number (PRINT) Do not turn this page until instructed to begin INSTRUCTIONS TO STUDENTS 1. During the exam, you are NOT PERMITTED to use: a. Electronic organizers b. Cell phones c. Pagers d. Headphones e. Any paper or other reference materials you brought into the room (books, notes, blank paper) 2. No extra time will be provided. When the end of the exam is announced, all students must stop writing and hand in their papers immediately to avoid penalties. 3. Please return all pages of this exam booklet. 4. Scrap paper is not permitted. If you need more space, use the back of the page of this exam booklet. 5. If you bring a programmable calculator to the exam, you must clear the memory before the exam begins. 6. Bring your photo ID to the exam. 7. This examination consists of 8 multiple-choice questions worth 8 points and two short-answer questions for 22 points. Altogether, there are 30 points. Please remember to show all your work in the short-answer questions in the given space. Correct but unsupported answers for those questions may be assigned a score of zero. 8. This examination consists of 6 pages , including this cover sheet. Please check the page numbers as you do the exam. PLEASE CHECK THAT YOU HAVE A COMPLETE EXAM

2 On this page , please record answers to the multiple-choice questions. Markings on the question pages will not be graded. 1. a. b. c. d. 2. a . b. c. d. 3. a. b. c. d. 4. a. b. c. d . 5. a. b. c. d. 6. a. b. c. d. 7. a . b. c. d. 8. a. b. c. d. The rest of this page is for the use of the Instructor Number of correct answers: × 1 = (out of 8) Part B: Short Answer Questions: Part B Question Number Points obtained 1 2 Total Points in Part B (out of 22) Total Points Obtained: out of 30.

4 6. The degrees of freedom for a chi-square test for independence where the different categories of the 2 variables are placed in a table with 7 rows and 4 columns is a. 28 b. 11 c. 9 d. 18 7. Which of the following tests is used to determine whether a set of additional variables significantly contributes to a multiple regression model? a) a t-test b) a Z test c) a partial F test d) a chi-square test 8. An analyst collected data on x and y variables and fitted a least-squares regression line. The resulting equation is 𝑦𝑦 � = −2.29 +1.70 ( x ). What is the residual for points (x = 5, y = 6)? (a ) −2.91 (b ) −0.21 (c) 0.21 (d) 6.21

5 Part B: Short answer questions. Please answer each question. They have equal points. Show all calculations and explanations. Correct answers without proper derivation and calculation will receive a grade of zero. (20 total points) 1. (10 points) An analyst examines the effect of various variables on crop yield. He estimates y = β 0 + β 1 x 1 + β 2 x 2 + β 3 x 3 + ε . where y is the average yield in bushels per acre, x 1 is the amount of summer rainfall, x 2 is the average daily use in machine hours of tractors on the farm, and x 3 is the amount of fertilizer used per acre. The partial excel output resulting from the regression analysis is as follows: df SS MS F Significance F Regression 3 12,000 4,000 Residual 6 2,400 400 Total 9 14,400 Coefficients Standard Error t-stat p-value Intercept 1.6 1.0 1.6 0.1232 x 1 7.5 2.5 3.0 0.0064 x 2 6.0 4.0 1.5 0.1472 x 3 1.0 0.5 2.0 0.0574 a) What is the fitted regression equation? b) At the 5% significance level, are the explanatory variables jointly significant in explaining crop yield? Explain. c) At the 5% significance level, is the amount of summer rainfall significant in explaining crop yield? Explain. Solution: a. 𝑦𝑦 � = 1.6 + 7.5 𝑥𝑥 1 + 6 𝑥𝑥 2 + 𝑥𝑥 3 b. The null and alternate hypotheses for a joint significance test of the three explanatory variables take the form: H 0 : β 1 = β 2 = β 3 = 0; H A : At least one β j ≠ 0. The appropriate test statistic is F with degrees of freedom (3, 6). The observed value of this F-statistic is F = MSR/MSE = 4000/400 = 10. From the table, the critical value is F (3,6);(0.05) = 4.76. Since the observed value of F = 10 > 4.76, we reject H 0 and conclude that at least one of the explanatory variables is significant in explaining crop yield. c. The null and alternate hypotheses for an individual significance test of summer rainfall ( x 1 ) take the form: H 0 : β 1 = 0; H A : β 1 ≠ 0. The p -value associated with x 1 is given as 0.0064, which is less than α (= 0.05). Hence, we reject H 0 and conclude that summer rainfall is significant in explaining crop yield.