A B C Who Jones X 2 67 58 83 3 59 78 59 4 100 64 95 5 81 68 71 6 80 79 81 7 63 68 92 8 100 86 92 9 44 48 84 10 82 61 83 11 67 73 73 12 81 51 84 13 74 56 77 14 99 51 84 15 58 46 74 16 99 93 78 17 98 59 79 18 65 66 72 19 72 64 79 20 50 92 98 21 72 62 90 22 63 73 91 23 83 83 62 24 80 66 82 25 69 71 74 26 79 85 63 27 77 64 86 28 63 71 95 29 70 54 76 30 66 79 64 31 89 88 59 32 75 81 85 33 87 82 45 34 86 61 91 35 58 81 68 36 72 80 74 37 73 73 100 38 85 65 66 39 70 98 88 40 71 62 81 41 59 100 72 42 77 93 68 43 92 83 65 44 72 70 96 45 82 38 98 46 62 72 89 47 79 75 81 48 92 70 53 49 71 67 100 50 96 76 57 51 81 97 74 52 61 61 95Question 1 - Midterm Scores A Business School offers multiple sections of a second-year introduction to statistics course, which is taught by three instructors. Their names are Dr. Who, Dr. Jones (Jr.), and Prof. X. The dataset Midterm Scores contains the midterm scores of a random sample of students who took the course with one of these instructors over the last several years. The Business School would like to determine whether the average midterm score differs among these three instructors. a) Create a side-by-side boxplot of the data and explain whether the similar variance and the nearly normality conditions for conducting an ANOVA seem to be satisfied. b) In addition to a side-by-side boxplot, what other graphs can you use to check whether the conditions for using an ANOVA are satisfied? Note: You don't need to produce the graphs; only explain how you would produce them. Answer the following questions, with exception of part g), assuming that the conditions for conducting an ANOVA are satisfied. c) Use software to calculate the sample variance for each instructor and then use it to calculate the pooled variance manually. Verify that your pooled variance value is the same as the MSE value displayed in the partial ANOVA table in part d) below. d) Fill in manually the missing values (1) to (6) in the ANOVA table below. Show your computations (maximum of 2 decimal places). Check your results using software. ANOVA Source of Variation SS df MS F p-value Between Groups (1) 2 (2) (3) (4) Within Groups (5) (6) 181.89 Total 28733.35 152 e) Use the one-way ANOVA table you produced in part d) to test whether there is a significant difference in the true mean midterm score among the three instructors. Use the critical value approach and a 5% confidence level. Make sure you follow all the steps for hypothesis testing indicated in the Instructions section above, show your computations, and state the business significance of your conclusion. f) Use the Bonferroni method for multiple comparisons to determine which population means differ (if any) at a = 0.05. Show your computations and clearly state your conclusion for each pairwise comparison. g) Perform a Kruskal-Wallis non-parametric test to determine whether there is a difference in the midterm scores across the three instructors. Use a 5% significance level and the critical value approach. You can use statistical software to run the test but remember to show all the steps for hypothesis testing indicated in the Instructions section. Is your conclusion consistent with your results in part e) above