11 special instructions: Provide all answers properly rounded to 2 decimal places of accuracy when expressed as a percentage or the equivalent decimal representation, i.e., 2/3 = 66.67% = 0.6667. Trailing zeroes do not need to be displayed, i.e., 1/10 = 10% = 0.10, 1/8 = 12.5% = 0.125. Single Factor ANOVA questions are expected to be computed manually, using the formulas presented in class, but Excel can be used for column sums, sums of squares, etc., followed by using Excel to verify the calculations. (provide output of the Excel ANOVA test) Block Design and Two Factor ANOVA are to be done using Excel. When necessary to convert any output to Single Factor ANOVA, these conversions are to be done manually. However, exact p-values and critical F values are to be obtained using Excel, even for manual calculations and conversions. When using the results to answer the questions, you are expected to provide the complete statistical process: Appropriate Hypotheses, critical values and rejection regions, and interpretation of the results in the context of the business questions being asked. Also provide the Excel ANOVA output. Question 1 A consumer safety group wanted to examine the factors contributing to road rage. A study was conducted with 100 drivers in each of educational categories: (1) High School diploma or less (HS), (2) up to 3 years of Post Secondary Education (PSE<3), and (3) more than 3 years of Post Secondary Education (PSE>3). Each respondent was given a questionnaire about their response to driving situations that scored them from 1 to 100. (a) Test to see if there are significant differences between drivers based on their level of educational attainment, using the following values Mean Standard Deviation n (b) HS 54.31 5.7817 100 PSE<3 56.29 5.7932 100 pse>3 54.11 6.3531 100 Grand 54.9033... 6.0428 300 In addition, the sample was structured so that for each level of educational achievement, there were 25 drivers in each of four age groups: 20-29, 20-45, 46-60 and Over 60. The data organized by age group can be found on Tab Q1b of the A11 Data.xls tab. Use Excel to test to see if both Age and education are significant factors in determining road rage. Question 2 The Operations Manager of a parts manufacturing plant noticed that late morning productivity was substantially lower than the first hour of the shift, and interested in the impact that breakfast would have on productivity. 30 employees agreed to allow the company supply breakfast for 4 weeks. Each week, each employee was assigned a different breakfast room where they got either (1) a cereal high in fiber and Protein (FPC), or (2) toast, grilled ham and egg (TGHE), or (3) a muffin with fruit and bran (M) or (4) donuts or pastries. The employees' productivity was measured between 8:30 and 9:30 and a second time, between 11:00 and 12:00 noon. The difference is the response variable that you will find on tab Q2 in the A11 Data File. A positive value means that productivity was lower later in the afternoon. Use Excel to test to see if the type of breakfast influences productivity. Question 3 There is little question that winter tires improve winter traction compared to all-season tires, but some consumer advocates suggest that the type of drivetrain can be just as important, if not more. Three types of tires (Aggressive Winter, AW; Performance Winter, PW; and All-seaon, AS) were tested on vehicles with four types of drivetrains (front-wheel drive, FWD; four wheel drive, 4WD; all wheel drive, AWD; and rear wheel drive, RWD). Stopping distance was measured at various speeds and combined into an overall index value for each vehicle, with the following results: Analyse and interpret the output thoroughly and manually make any changes that might be necessary. Question 4 Are there significant differences in business schools? One measure of school quality is the average salary of students 5 years after graduation. However, some point out that this measure can be greatly influenced by the mix of disciplines. For example, accounting students tend to make less during their first few years, but catch up and surpass many of their classmates years down the road. To control for this, students were chosen from 4 disciplines, marketing, finance, accounting, and operations form four schools, labeled A, B, C, and D. Their salaries 5 years after graduation were recorded and can be found on the Q4 tab of the A11 Data.xls file. Perform a Two-Way ANOVA test to determine whether there are differences between the business schools, controlling for discipline. Analyse and interpret the output thoroughly and manually make any changes that might be necessary. Age Group 20-29 30-45 HS 50 53 51 49 52 51 54 53 50 51 52 50 56 54 55 51 51 51 51 51 48 53 52 51 54 63 61 59 63 59 58 64 61 60 65 56 60 64 62 65 62 64 62 64 57 Education Level PSE<3 pse>3 52 48 55 54 52 50 51 48 54 52 53 51 55 55 54 54 52 49 52 51 54 53 52 48 56 56 55 54 56 56 52 50 52 50 53 51 52 50 53 51 51 47 54 53 54 53 53 51 55 54 65 62 63 61 61 60 65 62 62 61 61 60 67 63 64 62 63 61 67 63 59 57 63 61 65 62 65 62 67 63 64 62 65 62 64 62 65 62 60 58 46-60 60+ 63 60 61 63 60 57 58 55 56 56 56 55 59 58 59 58 57 60 55 60 56 56 56 58 55 58 58 58 56 55 47 47 47 51 46 45 52 46 46 50 48 45 45 48 45 45 47 47 65 62 63 65 63 59 61 56 57 57 57 55 62 60 62 61 59 62 56 62 57 58 58 60 56 61 61 60 57 55 50 49 50 52 49 47 54 48 48 52 51 47 47 51 47 48 50 50 62 61 62 62 61 58 60 56 57 56 57 55 60 58 60 59 58 61 56 61 57 57 57 58 55 60 59 59 57 55 45 45 46 49 45 43 52 45 44 48 47 44 44 47 43 44 47 46 47 47 49 45 46 47 48 49 50 51 47 48 49 51 45 46 48 43 44 45 47 Employee 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 FPC 9 15 6 2 7 13 4 3 8 4 10 12 5 12 4 4 9 12 11 13 6 4 5 3 16 2 14 6 10 8 TGHE 7 8 5 2 -1 7 2 2 10 1 8 9 7 6 5 5 7 11 6 11 5 2 5 4 10 5 7 5 10 6 M 11 14 4 5 4 10 5 8 11 2 16 11 13 12 5 8 12 13 11 16 11 7 8 2 15 13 9 11 14 10 D 8 17 13 9 7 16 5 2 11 5 11 16 14 14 5 6 17 11 13 14 5 4 13 7 16 4 7 14 15 10 Mtkg Fine Acct Ops A 112.0 82.2 79.8 106.3 96.0 107.7 80.5 111.7 109.5 88.5 108.8 112.1 87.1 130.1 123.7 147.4 107.6 85.0 119.6 85.7 127.7 115.0 122.3 145.2 83.5 99.9 89.8 87.0 93.0 108.2 94.9 86.0 82.2 100.5 91.1 89.2 128.1 116.5 81.4 99.3 120.8 80.4 93.3 128.6 102.1 85.4 95.4 70.6 B 80.4 91.1 75.5 82.4 88.0 94.7 99.7 121.4 91.1 104.4 118.5 92.2 109.9 128.8 111.4 136.3 141.0 121.6 114.6 105.9 120.5 126.1 143.5 87.7 96.3 99.8 87.1 94.1 95.1 104.5 96.2 82.3 93.5 106.0 101.5 80.0 108.4 106.7 109.6 135.9 127.0 78.6 135.6 138.7 119.4 75.6 96.8 116.1 C 109.5 76.7 109.7 124.6 104.6 81.5 79.6 95.5 95.6 79.0 121.1 112.3 99.8 99.6 90.3 91.1 93.3 125.9 133.3 95.7 134.2 125.8 133.3 120.6 94.6 92.4 82.8 100.7 105.8 102.1 95.2 82.5 103.2 104.0 98.1 91.5 97.9 109.7 114.8 78.9 131.1 95.3 122.3 118.0 114.8 70.4 105.9 137.1 D 109.7 84.7 112.1 86.3 76.4 76.1 83.7 83.5 104.2 122.1 86.0 85.6 110.4 93.2 106.7 89.9 149.7 134.2 146.9 140.5 98.7 105.9 115.5 93.7 90.7 102.9 107.9 100.7 105.3 100.9 100.7 108.6 86.8 83.3 84.6 91.4 101.0 127.7 110.2 120.0 76.8 89.5 120.1 87.0 121.5 75.0 126.6 87.4