1 D E F G 1 2 0 1 2 5 75 14 31 32 33 34 25 36 37 38 39 40 41 42 43 44 28 BO 50 28 100 28 SO 108 64 16 26 18 15 31 16 20 1 3 1 1 2 1 1 1 3 2 2 1 2 1 2 1 1 1 2 1 1 2 2 1 An experiment was conducted in order to evaluate the effectiveness of two devices for improving the efficiency of car engine systems Engine efficacy was measured after one of the two devices was fixed The two devices were an electric vent 200F (200F) and electric vent 1495 (1498) The Engine efficacy data (BTU In) are stacked in one column with a grouping column (Vent type) containing identifiers or subscripts to denote the population See attached excel file on tab (car engine) Suppose that you performed a variance test and found no evidence for variances being unequal Test the normality assumption (by graph and goodness of fit) and Show your work using confidence interval and hypothesis testing procedures to test the variances equality (Solve manually and Minitab) 2 1 1 99 34 HO 99 99 6 SO 10 2 28 2 1 1 2 2 3 9 28 1 2 1 3 3 2 45 46 47 48 1 1 1 1 1 2 99 15 45 688888888888 H 9 82 12 91 10 35 9 6 9 58 9 83 9 52 18 26 10 64 6 62 5 2 12 28 7 23 2 97 8 81 9 27 11 29 8 29 9 96 10 3 16 06 14 24 11 43 10 28 13 6 5 94 10 36 6 85 6 72 10 21 25 26 16 32 16 18 20 31 39 15 32 25 21 23 20 16 17 31 27 14 1 J 10 55 200 F 13 89 200 F 10 72 200 F 9 22 200 F 10 61 200 F 10 04 200 F 10 2 200 F 20 55 200 11 75 200 F 7 08 200 F 5 5 200 13 07 1495 7 6 1495 3 2 1495 9 28 1495 9 73 1495 11 73 1495 9 67 1495 10 76 1495 11 05 1495 17 63 1495 15 58 1495 12 53 1498 11 87 1495 14 19 149 6 BA 1495 11 89 1495 7 41 1495 7 42 1495 10 83 1495 72 70 28 72 96 49 100 49 Now you want to compare the effectiveness of these two devices by determining whether or not there is any evidence that the difference between the devices is different from zero (Solve manually and Minitab) 50 51 52 53 2 1 2 2 2 9 1 30 40 50 60 12 1 3 1 3 3 2 2 2 1 1 1 3 1 3 1 1 2 2 1 1 55 56 57 58 59 60 28 38 72 28 1 1 1 2 2 1 2 1 99 90 F 55 1 2 2 28 17 1 2 2 3 E F 5 64 D 16 28 1 61 62 63 1 2 2 2 1 2 28 1 65 66 67 17 29 12 20 22 2 O 2 1 D O H 8 61 11 62 11 21 10 95 7 62 10 4 12 92 15 12 12 47 12 S5 28 12 80 19 32 99 60 65 15 SS 3 1 1 1 2 90 AD 64 30 1 1 1 B D E CH Area CH Shape CH HT CH Liner Car 28 1 20 2 144 2 26 0 80 3 30 1 100 2 24 o 168 3 35 1 1 28 1 17 2 64 2 24 1 64 2 18 1 96 3 3 25 1 108 3 27 1 64 2 16 1 63 3 3 30 1 42 3 15 1 117 3 25 O 64 2 18 1 28 1 17 2 64 2 28 0 64 2 19 1 28 1 26 2 80 3 3 27 0 0 28 1 14 2 28 1 23 2 64 2 17 1 30 64 2 27 0 64 2 19 1 50 1 18 1 50 1 18 1 50 1 18 1 11 7 7 73 1 9 44 1495 1294 1495 13 15 1495 11 69 1495 7 73 1495 11 94 1495 13 62 1495 17 07 1495 14 66 1495 956 1495 12 37 1495 8 33 1495 8 67 1495 11 27 1495 11 67 1495 9 37 1495 8 93 1495 G Monthes used 3 8 2 75 2 2 44 2 75 2 30 3 2 45 1 16 5 45 5 40 1 22 2 40 1 13 2 2 99 1 19 2 30 2 60 2 30 2 10 2 60 1 24 2 70 1 1 12 2 60 2 40 1 17 4 15 1 1 18 1 4 H BTU In 7 87 9 43 7 16 8 67 12 31 9 84 16 9 10 04 12 62 7 62 11 12 13 43 9 07 6 94 10 28 9 37 7 93 13 96 6 8 4 8 58 8 5 98 15 24 8 54 11 09 11 7 12 71 6 78 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 70 71 22 73 J BTU Out Vent type 8 25 200 F 9 66 200 F 8 33 200 F 8 82 200 F 12 06 200 9 67 200 F 17 51 200 F 10 79 200 F 13 59 200 F 7 99 200 F 12 64 200 F 14 42 200 F 9 25 200 F 7 79 200 F 11 29 200 F 10 26 200 F 9 46 200 F 14 77 200 F 7 21 200 F 4 29 200 F 9 81 200 F 8 41 200 F 6 78 200 F 16 3 200 F 9 01 200 F 11 41 200 F 12 37 200 F 13 28 200 F 7 24 200 F 50 SD 28 SD SD 50 SD 13 10 1 76 27 78 79 BD 19 15 18 18 15 16 17 15 1 1 1 5 28 28 2 2 1 1 1 1 1 2 1 1 1 1 1 2 1 2 2 2 1 2 1 2 2 1 1 1 1 1 2 2 2 1 2 2 1 O O SO 82 83 28 49 100 10 14 40 70 7 29 10 49 8 60 8 26 7 69 12 19 5 56 9 76 7 15 12 69 13 38 13 11 10 5 14 35 13 42 635 9 83 12 16 30 17 18 27 22 30 24 17 20 20 28 85 86 87 88 89 90 91 ANN 1 1 1 1 1 2 2 1 2 1 2 12 85 1495 5 27 1495 10 02 1495 7 87 1495 11 82 1495 14 42 1495 13 69 1495 10 77 1495 15 26 1495 14 53 1495 6 84 1495 10 92 1495 13 05 1495 100 96 100 100 28 O 0 1 1 1 70 40 99 14 55 1 D E F G 1 2 0 1 2 5 75 14 31 32 33 34 25 36 37 38 39 40 41 42 43 44 28 BO 50 28 100 28 SO 108 64 16 26 18 15 31 16 20 1 3 1 1 2 1 1 1 3 2 2 1 2 1 2 1 1 1 2 1 1 2 2 1 An experiment was conducted in order to evaluate the effectiveness of two devices for improving the efficiency of car engine systems Engine efficacy was measured after one of the two devices was fixed The two devices were an electric vent 200F (200F) and electric vent 1495 (1498) The Engine efficacy data (BTU In) are stacked in one column with a grouping column (Vent type) containing identifiers or subscripts to denote the population See attached excel file on tab (car engine) Suppose that you performed a variance test and found no evidence for variances being unequal Test the normality assumption (by graph and goodness of fit) and Show your work using confidence interval and hypothesis testing procedures to test the variances equality (Solve manually and Minitab) 2 1 1 99 34 HO 99 99 6 SO 10 2 28 2 1 1 2 2 3 9 28 1 2 1 3 3 2 45 46 47 48 1 1 1 1 1 2 99 15 45 688888888888 H 9 82 12 91 10 35 9 6 9 58 9 83 9 52 18 26 10 64 6 62 5 2 12 28 7 23 2 97 8 81 9 27 11 29 8 29 9 96 10 3 16 06 14 24 11 43 10 28 13 6 5 94 10 36 6 85 6 72 10 21 25 26 16 32 16 18 20 31 39 15 32 25 21 23 20 16 17 31 27 14 1 J 10 55 200 F 13 89 200 F 10 72 200 F 9 22 200 F 10 61 200 F 10 04 200 F 10 2 200 F 20 55 200 11 75 200 F 7 08 200 F 5 5 200 13 07 1495 7 6 1495 3 2 1495 9 28 1495 9 73 1495 11 73 1495 9 67 1495 10 76 1495 11 05 1495 17 63 1495 15 58 1495 12 53 1498 11 87 1495 14 19 149 6 BA 1495 11 89 1495 7 41 1495 7 42 1495 10 83 1495 72 70 28 72 96 49 100 49 Now you want to compare the effectiveness of these two devices by determining whether or not there is any evidence that the difference between the devices is different from zero (Solve manually and Minitab) 50 51 52 53 2 1 2 2 2 9 1 30 40 50 60 12 1 3 1 3 3 2 2 2 1 1 1 3 1 3 1 1 2 2 1 1 55 56 57 58 59 60 28 38 72 28 1 1 1 2 2 1 2 1 99 90 F 55 1 2 2 28 17 1 2 2 3 E F 5 64 D 16 28 1 61 62 63 1 2 2 2 1 2 28 1 65 66 67 17 29 12 20 22 2 O 2 1 D O H 8 61 11 62 11 21 10 95 7 62 10 4 12 92 15 12 12 47 12 S5 28 12 80 19 32 99 60 65 15 SS 3 1 1 1 2 90 AD 64 30 1 1 1 B D E CH Area CH Shape CH HT CH Liner Car 28 1 20 2 144 2 26 0 80 3 30 1 100 2 24 o 168 3 35 1 1 28 1 17 2 64 2 24 1 64 2 18 1 96 3 3 25 1 108 3 27 1 64 2 16 1 63 3 3 30 1 42 3 15 1 117 3 25 O 64 2 18 1 28 1 17 2 64 2 28 0 64 2 19 1 28 1 26 2 80 3 3 27 0 0 28 1 14 2 28 1 23 2 64 2 17 1 30 64 2 27 0 64 2 19 1 50 1 18 1 50 1 18 1 50 1 18 1 11 7 7 73 1 9 44 1495 1294 1495 13 15 1495 11 69 1495 7 73 1495 11 94 1495 13 62 1495 17 07 1495 14 66 1495 956 1495 12 37 1495 8 33 1495 8 67 1495 11 27 1495 11 67 1495 9 37 1495 8 93 1495 G Monthes used 3 8 2 75 2 2 44 2 75 2 30 3 2 45 1 16 5 45 5 40 1 22 2 40 1 13 2 2 99 1 19 2 30 2 60 2 30 2 10 2 60 1 24 2 70 1 1 12 2 60 2 40 1 17 4 15 1 1 18 1 4 H BTU In 7 87 9 43 7 16 8 67 12 31 9 84 16 9 10 04 12 62 7 62 11 12 13 43 9 07 6 94 10 28 9 37 7 93 13 96 6 8 4 8 58 8 5 98 15 24 8 54 11 09 11 7 12 71 6 78 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 70 71 22 73 J BTU Out Vent type 8 25 200 F 9 66 200 F 8 33 200 F 8 82 200 F 12 06 200 9 67 200 F 17 51 200 F 10 79 200 F 13 59 200 F 7 99 200 F 12 64 200 F 14 42 200 F 9 25 200 F 7 79 200 F 11 29 200 F 10 26 200 F 9 46 200 F 14 77 200 F 7 21 200 F 4 29 200 F 9 81 200 F 8 41 200 F 6 78 200 F 16 3 200 F 9 01 200 F 11 41 200 F 12 37 200 F 13 28 200 F 7 24 200 F 50 SD 28 SD SD 50 SD 13 10 1 76 27 78 79 BD 19 15 18 18 15 16 17 15 1 1 1 5 28 28 2 2 1 1 1 1 1 2 1 1 1 1 1 2 1 2 2 2 1 2 1 2 2 1 1 1 1 1 2 2 2 1 2 2 1 O O SO 82 83 28 49 100 10 14 40 70 7 29 10 49 8 60 8 26 7 69 12 19 5 56 9 76 7 15 12 69 13 38 13 11 10 5 14 35 13 42 635 9 83 12 16 30 17 18 27 22 30 24 17 20 20 28 85 86 87 88 89 90 91 ANN 1 1 1 1 1 2 2 1 2 1 2 12 85 1495 5 27 1495 10 02 1495 7 87 1495 11 82 1495 14 42 1495 13 69 1495 10 77 1495 15 26 1495 14 53 1495 6 84 1495 10 92 1495 13 05 1495 100 96 100 100 28 O 0 1 1 1 70 40 99 14 55

Question

1 D E F G 1 2 0 1 2 5 75 14 31 32 33 34 25 36 37 38 39 40 41 42 43 44 28 BO 50 28 100 28 SO 108 64 16 26 18 15 31 16 20 1 3 1 1 2  1 1 1 3 2 2 1 2 1 2 1 1 1 2 1 1 2 2 1  An experiment was conducted in order to evaluate the effectiveness of two devices for improving the efficiency of car engine systems  Engine efficacy was measured after one of the two devices was fixed  The two devices were an electric vent 200F (200F) and electric vent 1495 (1498)  The Engine efficacy data (BTU In) are stacked in one column with a grouping column (Vent type) containing identifiers or subscripts to denote the population  See attached excel file on tab (car engine) Suppose that you performed a variance test and found no evidence for variances being unequal   Test the normality assumption (by graph and goodness of fit) and Show your work using confidence interval and hypothesis testing procedures to test the variances equality  (Solve manually and Minitab) 2 1 1 99 34 HO 99 99 6 SO 10 2 28 2 1 1 2 2 3 9 28 1 2 1 3 3 2 45 46 47 48 1 1 1 1 1 2 99 15 45 688888888888 H 9 82 12 91 10 35 9 6 9 58 9 83 9 52 18 26 10 64 6 62 5 2 12 28 7 23 2 97 8 81 9 27 11 29 8 29 9 96 10 3 16 06 14 24 11 43 10 28 13 6 5 94 10 36 6 85 6 72 10 21 25 26 16 32 16 18 20 31 39 15 32 25 21 23 20 16 17 31 27 14 1 J 10 55 200 F 13 89 200 F 10 72 200 F 9 22 200 F 10 61 200 F 10 04 200 F 10 2 200 F 20 55 200 11 75 200 F 7 08 200 F 5 5 200  13 07 1495 7 6 1495 3 2 1495 9 28 1495 9 73 1495 11 73 1495 9 67 1495 10 76 1495 11 05 1495 17 63 1495 15 58 1495 12 53 1498 11 87 1495 14 19 149 6 BA 1495 11 89 1495 7 41 1495 7 42 1495 10 83 1495 72 70 28 72 96 49 100 49 Now you want to compare the effectiveness of these two devices by determining whether or not there is any evidence that the difference between the devices is different from zero    (Solve manually and Minitab) 50 51 52 53 2 1 2 2 2  9 1 30 40 50 60 12 1 3 1 3 3 2 2 2 1 1 1 3 1 3 1 1 2 2 1 1 55 56 57 58 59 60 28 38 72 28 1 1 1 2 2 1 2 1 99 90 F 55 1 2  2 28 17 1 2 2 3 E F 5 64 D 16 28 1 61 62 63 1 2 2 2 1 2 28 1 65 66 67 17 29 12 20 22 2 O 2 1 D O H 8 61 11 62 11 21 10 95 7 62 10 4 12 92 15 12 12 47 12 S5 28 12 80 19 32 99 60 65 15 SS 3 1 1 1 2 90 AD 64 30 1 1 1 B D E CH Area CH Shape CH HT CH Liner Car 28 1 20 2 144 2 26 0 80 3 30 1 100 2 24 o 168 3 35 1 1 28 1 17 2 64 2 24 1 64 2 18 1 96 3 3 25 1 108 3 27 1 64 2 16 1 63 3 3 30 1 42 3 15 1 117 3 25 O 64 2 18 1 28 1 17 2 64 2 28 0 64 2 19 1 28 1 26 2 80 3 3 27 0 0 28 1 14 2 28 1 23 2 64 2 17 1 30 64 2 27 0 64 2 19 1 50 1 18 1 50 1 18 1 50 1 18 1 11 7 7 73 1 9 44 1495 1294 1495 13 15 1495 11 69 1495 7 73 1495 11 94 1495 13 62 1495 17 07 1495 14 66 1495 956 1495 12 37 1495 8 33 1495 8 67 1495 11 27 1495 11 67 1495 9 37 1495 8 93 1495 G Monthes used 3 8 2 75 2 2 44 2 75 2 30 3 2 45 1 16 5 45 5 40 1 22 2 40 1 13 2 2 99 1 19 2 30 2 60 2 30 2 10 2 60 1 24 2 70 1 1 12 2 60 2 40 1 17 4 15 1 1 18 1 4 H BTU In 7 87 9 43 7 16 8 67 12 31 9 84 16 9 10 04 12 62 7 62 11 12 13 43 9 07 6 94 10 28 9 37 7 93 13 96 6 8 4 8 58 8 5 98 15 24 8 54 11 09 11 7 12 71 6 78 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 70 71 22 73 J BTU Out Vent type 8 25 200 F 9 66 200 F 8 33 200 F   8 82 200 F 12 06 200  9 67 200 F 17 51 200 F 10 79 200 F 13 59 200 F 7 99 200 F 12 64 200 F 14 42 200 F 9 25 200 F 7 79 200 F 11 29 200 F 10 26 200 F 9 46 200 F 14 77 200 F 7 21 200 F 4 29 200 F 9 81 200 F 8 41 200 F   6 78 200 F 16 3 200 F 9 01 200 F 11 41 200 F 12 37 200 F 13 28 200 F 7 24 200 F   50 SD 28 SD SD 50 SD 13 10 1 76 27 78 79 BD 19 15 18 18 15 16 17 15 1 1 1 5 28 28 2 2 1 1 1 1 1 2 1 1 1 1 1 2 1 2 2 2   1 2 1 2 2 1 1 1 1 1 2 2 2 1 2 2 1 O O SO 82 83 28 49 100 10 14 40 70 7 29 10 49 8 60 8 26 7 69 12 19 5 56 9 76 7 15 12 69 13 38 13 11 10 5 14 35 13 42 635 9 83 12 16 30 17 18 27 22 30 24 17 20 20 28 85 86 87 88 89 90 91 ANN 1 1 1 1 1 2 2 1 2 1 2 12 85 1495 5 27 1495 10 02 1495 7 87 1495 11 82 1495 14 42 1495 13 69 1495 10 77 1495 15 26 1495 14 53 1495 6 84 1495 10 92 1495 13 05 1495 100 96 100 100 28 O 0 1 1 1 70 40 99 14 55   1 D E F G 1 2 0 1 2 5 75 14 31 32 33 34 25 36 37 38 39 40 41 42 43 44 28 BO 50 28 100 28 SO 108 64 16 26 18 15 31 16 20 1 3 1 1 2  1 1 1 3 2 2 1 2 1 2 1 1 1 2 1 1 2 2 1  An experiment was conducted in order to evaluate the effectiveness of two devices for improving the efficiency of car engine systems  Engine efficacy was measured after one of the two devices was fixed  The two devices were an electric vent 200F (200F) and electric vent 1495 (1498)  The Engine efficacy data (BTU In) are stacked in one column with a grouping column (Vent type) containing identifiers or subscripts to denote the population  See attached excel file on tab (car engine) Suppose that you performed a variance test and found no evidence for variances being unequal   Test the normality assumption (by graph and goodness of fit) and Show your work using confidence interval and hypothesis testing procedures to test the variances equality  (Solve manually and Minitab) 2 1 1 99 34 HO 99 99 6 SO 10 2 28 2 1 1 2 2 3 9 28 1 2 1 3 3 2 45 46 47 48 1 1 1 1 1 2 99 15 45 688888888888 H 9 82 12 91 10 35 9 6 9 58 9 83 9 52 18 26 10 64 6 62 5 2 12 28 7 23 2 97 8 81 9 27 11 29 8 29 9 96 10 3 16 06 14 24 11 43 10 28 13 6 5 94 10 36 6 85 6 72 10 21 25 26 16 32 16 18 20 31 39 15 32 25 21 23 20 16 17 31 27 14 1 J 10 55 200 F 13 89 200 F 10 72 200 F 9 22 200 F 10 61 200 F 10 04 200 F 10 2 200 F 20 55 200 11 75 200 F 7 08 200 F 5 5 200  13 07 1495 7 6 1495 3 2 1495 9 28 1495 9 73 1495 11 73 1495 9 67 1495 10 76 1495 11 05 1495 17 63 1495 15 58 1495 12 53 1498 11 87 1495 14 19 149 6 BA 1495 11 89 1495 7 41 1495 7 42 1495 10 83 1495 72 70 28 72 96 49 100 49 Now you want to compare the effectiveness of these two devices by determining whether or not there is any evidence that the difference between the devices is different from zero    (Solve manually and Minitab) 50 51 52 53 2 1 2 2 2  9 1 30 40 50 60 12 1 3 1 3 3 2 2 2 1 1 1 3 1 3 1 1 2 2 1 1 55 56 57 58 59 60 28 38 72 28 1 1 1 2 2 1 2 1 99 90 F 55 1 2  2 28 17 1 2 2 3 E F 5 64 D 16 28 1 61 62 63 1 2 2 2 1 2 28 1 65 66 67 17 29 12 20 22 2 O 2 1 D O H 8 61 11 62 11 21 10 95 7 62 10 4 12 92 15 12 12 47 12 S5 28 12 80 19 32 99 60 65 15 SS 3 1 1 1 2 90 AD 64 30 1 1 1 B D E CH Area CH Shape CH HT CH Liner Car 28 1 20 2 144 2 26 0 80 3 30 1 100 2 24 o 168 3 35 1 1 28 1 17 2 64 2 24 1 64 2 18 1 96 3 3 25 1 108 3 27 1 64 2 16 1 63 3 3 30 1 42 3 15 1 117 3 25 O 64 2 18 1 28 1 17 2 64 2 28 0 64 2 19 1 28 1 26 2 80 3 3 27 0 0 28 1 14 2 28 1 23 2 64 2 17 1 30 64 2 27 0 64 2 19 1 50 1 18 1 50 1 18 1 50 1 18 1 11 7 7 73 1 9 44 1495 1294 1495 13 15 1495 11 69 1495 7 73 1495 11 94 1495 13 62 1495 17 07 1495 14 66 1495 956 1495 12 37 1495 8 33 1495 8 67 1495 11 27 1495 11 67 1495 9 37 1495 8 93 1495 G Monthes used 3 8 2 75 2 2 44 2 75 2 30 3 2 45 1 16 5 45 5 40 1 22 2 40 1 13 2 2 99 1 19 2 30 2 60 2 30 2 10 2 60 1 24 2 70 1 1 12 2 60 2 40 1 17 4 15 1 1 18 1 4 H BTU In 7 87 9 43 7 16 8 67 12 31 9 84 16 9 10 04 12 62 7 62 11 12 13 43 9 07 6 94 10 28 9 37 7 93 13 96 6 8 4 8 58 8 5 98 15 24 8 54 11 09 11 7 12 71 6 78 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 70 71 22 73 J BTU Out Vent type 8 25 200 F 9 66 200 F 8 33 200 F   8 82 200 F 12 06 200  9 67 200 F 17 51 200 F 10 79 200 F 13 59 200 F 7 99 200 F 12 64 200 F 14 42 200 F 9 25 200 F 7 79 200 F 11 29 200 F 10 26 200 F 9 46 200 F 14 77 200 F 7 21 200 F 4 29 200 F 9 81 200 F 8 41 200 F   6 78 200 F 16 3 200 F 9 01 200 F 11 41 200 F 12 37 200 F 13 28 200 F 7 24 200 F   50 SD 28 SD SD 50 SD 13 10 1 76 27 78 79 BD 19 15 18 18 15 16 17 15 1 1 1 5 28 28 2 2 1 1 1 1 1 2 1 1 1 1 1 2 1 2 2 2   1 2 1 2 2 1 1 1 1 1 2 2 2 1 2 2 1 O O SO 82 83 28 49 100 10 14 40 70 7 29 10 49 8 60 8 26 7 69 12 19 5 56 9 76 7 15 12 69 13 38 13 11 10 5 14 35 13 42 635 9 83 12 16 30 17 18 27 22 30 24 17 20 20 28 85 86 87 88 89 90 91 ANN 1 1 1 1 1 2 2 1 2 1 2 12 85 1495 5 27 1495 10 02 1495 7 87 1495 11 82 1495 14 42 1495 13 69 1495 10 77 1495 15 26 1495 14 53 1495 6 84 1495 10 92 1495 13 05 1495 100 96 100 100 28 O 0 1 1 1 70 40 99 14 55

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