analyze the following problems in JMP and answer the questions below. 1. Given a recent outbreak of illness caused by E.coli bacteria, the mayor of a large city is concerned that some of his restaurant inspectors are not consistent with their evaluations of a restaurant cleanliness. In order to investigate this possibility, the mayor has five restaurant inspectors grade (scale of 0 to 100) the cleanliness of three restaurants. Restaurant Inspector 1 2 3 1 72 54 84 2 68 55 85 3 73 59 80 4 69 60 82 5 75 56 84 a. Perform some descriptive statistics on the data. What are the average cleanliness scores for the 3 restaurants and the average cleanliness score given by the 5 inspectors? b. State the model and all of the appropriate hypotheses being tested for this Two-way ANOVA problem c. Run a two-way ANOVA analysis and draw your conclusions. What is your conclusion about the average cleanliness score between the three restaurants? What is your conclusion about the effect of the 5 inspectors on the cleanliness score? Is there any interaction between the Factors? d. Check the residual plots and comment on the adequacy of the model. 2. It is generally believed that a practical major such as business or engineering can really pay off for college graduates (CNNMoney.com, July 2010). Other studies have shown that it is not just the major, but also how students perform, as measured by their GPA, that influences their salaries. Henry Chen, an employee of PayScale.com, wants to measure the effect of major and GPA on starting salaries of graduates of the University of California at Irvine. He samples the starting salaries of five graduates for a given GPA range from the schools of business, engineering, and social sciences. a. Perform some descriptive statistics on the data. What are the average salaries and standard deviations for the different grouping variables? Create a graph that summarizes the data (boxplot, bar graph or something similar). b. State the model and all of the appropriate hypotheses being tested for this Two-way ANOVA problem c. Run a two-way ANOVA, with GPA, school, and the interaction term. Is there an interaction between GPA range and the school of graduation? If so, interpret the interaction through an LSmeans plot and multiple comparison confidence intervals. If no interaction is present, draw your conclusion about starting salary between majors and your conclusion about the effect of GPA on starting salary. d. Calculate the salary prediction for the following categories of students i. An Engineering student with a 3.3 GPA ii. A Business student with a 3.9 GPA iii. A Social Science student with a 2.8 GPA GPA Business Engineering Social Sciences 3.5-4.0 68 70 44 54 66 52 78 62 66 3.0-3.5 < 3.0 80 58 48 76 60 48 64 54 42 66 58 66 56 72 66 54 70 52 64 60 42 48 59 65 42 72 48 48 58 56 38 44 38 42 52 50