Question 1. [15 marks] A statistics instructor noticed that the further the students were from him, the more likely they were to miss class or use an instant messenger during class. He suspected that this would affect their exam grades. In particular, he wanted to see if the students further away from him did worse on the exams. He divided the classroom into three rows: front, middle, and back. He then took a random sample of the students in each row and recorded their score on an exam. The results are shown in the Exam Grades file. a. For this experiment, identify the number of factors and the number of treatments. b. Do the data provide enough evidence to indicate an average difference in students’ grades based on where they are sitting in the classroom? Use the critical value approach, and a 5% level of significance. c. Show how the MSE can be calculated by pooling the three sample variances. d. The researcher believes that students sitting at the back of the classroom will do worse on the exam. As well, he believes that those in the middle will have worse grades than those at the front. Using the Bonferroni method, construct confidence intervals with an overall confidence level of 95% to make the appropriate comparisons. What do you conclude? e. Plot the residuals against the fitted values and comment on whether the two basic assumptions of the analysis of variance model are warranted. Question 2. [5 marks] To investigate the impact of training on its supervisorsâ€™ decision-making abilities, a company designed the following experiment. Sixteen supervisors were selected and eight were randomly chosen to receive managerial training. Then four of the trained supervisors and four of the untrained supervisors were randomly chosen and placed them in a situation where a standard problem arose. The other eight were faced with an emergency situation where standard procedures were ineffective. The managerial behaviour of the 16 supervisors was then recorded according to a specified scheme. a. What are the experimental units? b. What are the factors considered in the study? c. What are the levels of each of the factors? d. What is the number of treatments in the experiment? e. What type of experimental design was used in the study? Question 3. [20 marks] Farming is a risky business due to many factors out of the control of farmers, including natural disasters. To help protect farmers, Agriculture and Agri-Food Canada (AAFC) has designed four insurance programs, namely, A, B, C, and D. There are six premium schemes for the insurance programs: three with premiums of $150 or more and three with premiums less than $150. To test the popularity of these programs, AAFC designed a rating scheme on a scale from 1 to 100. The data are shown in the Agriculture Insurance Program file. For all tests of hypotheses, use the 5% level of significance and the critical value approach. a. What type of analysis was used to evaluate the programs? What are the factors? How many levels are used for each factor? How many treatments are there? b. Plot the treatment means against the factors and comment on the possibility of interaction and of main effects. c. Test for interaction between the factors. d. Does your conclusion in part c agree with your observations in part b? Explain why or why not. e. Test for a main effect due to the insurance program. f. Test for a main effect due to cost. g. Using the Bonferroni method, determine which insurance programs are statistically significantly different in average popularity. h. Plot the residuals against the fitted values and comment on whether the two basic assumptions of the analysis of variance model are warranted