The US Department of Energy\'s Fuel Economy Guide provides fuel efficiency data

Question

The US Department of Energy's Fuel Economy Guide provides fuel efficiency data for cars. A portion of the data is shown at the bottom of this worksheet. a. Do these data represent experimental or observational data? Explain and justify your answer. b. Describe the population that is represented by this sample. Justify your answer. c. How many observations are in this data set? d. How many variables are in this data set? e. How many data values are in this data set? f. Which of the variable(s) are quantitative? g. Which variables are categorical? h. Give an example of a question that could be answered by using descriptive statistics with these data. i. One consultant for a car rental company said: "We should stop offering large cars, based on their low MPG. They are just a waste of fuel.". Explain if the consultant is justified in making the statement. Car Size (1=Compact, 2=Midsize, 3=Large) Displacement Cylinders Drive Fuel Type City MPG Hwy MPG 1 1 2.0 4 F P 22 30 2 1 2.0 4 A P 21 29 3 1 2.0 4 A P 21 31 4 1 3.0 6 A P 18 28 5 1 3.0 6 A P 18 27 6 1 6.0 12 A P 12 19 7 1 4.4 8 R P 16 24 8 1 4.4 8 R P 15 22 9 1 3.6 6 R R 19 30 10 1 3.6 6 R R 18 29 11 1 3.6 6 R R 17 28 12 1 6.2 8 R R 15 24 13 1 6.2 8 R R 16 24 14 1 2.4 4 F R 18 29 15 1 3.6 6 F R 19 29 16 1 2.0 4 F R 28 38 17 1 2.0 4 F R 27 37 18 1 2.0 4 F R 26 36 19 1 2.0 4 F R 28 40 20 1 1.8 4 F R 28 39 21 1 1.8 4 F R 28 36 22 1 2.4 4 F P 22 31 23 1 1.8 4 F R 29 41 24 1 1.5 4 F R 44 44 25 1 1.6 4 F R 30 40 26 1 1.6 4 F R 30 40 27 1 2.5 4 F R 22 29 28 1 2.5 4 F R 20 28 29 1 4.7 8 R P 17 25 30 1 6.7 12 R P 11 18 31 1 6.7 12 R P 11 18 32 1 2.0 4 F R 18 28 33 1 2.0 4 F R 20 33 34 1 2.0 4 A R 18 29 35 1 2.0 4 A R 20 30 36 1 2.0 4 F R 19 29 37 1 2.0 4 F R 20 33 38 1 2.5 4 F R 23 31 39 1 2.5 4 F R 23 31 40 1 2.0 4 F P 22 31 41 1 2.0 4 F P 21 31 42 1 3.6 6 A P 17 25 43 1 2.5 5 F R 24 31 44 1 2.5 5 F R 23 33 45 1 2.0 4 F P 24 33 46 1 2.0 4 F P 21 31 47 1 2.0 4 F R 23 29 48 1 2.0 4 F P 24 32 49 1 2.0 4 F R 24 34 50 1 2.0 4 F P 22 33 51 1 2.5 5 F R 24 31 52 1 2.5 5 F R 23 33 53 1 2.5 5 F R 21 30 54 1 2.5 5 F R 21 29 55 1 3.0 6 A R 18 26 56 1 2.5 5 F R 20 30 57 2 3.5 6 F P 20 29 58 2 3.7 6 A P 18 26 59 2 3.7 6 A P 17 25 60 2 2.0 4 F P 25 33 61 2 2.0 4 F P 25 33 62 2 3.0 6 A P 19 28 63 2 3.0 6 A P 18 28 64 2 4.2 8 A P 18 28 65 2 6.0 12 A P 11 19 66 2 2.4 4 F R 25 36 67 2 3.6 6 F R 17 27 68 2 3.6 6 A R 16 26 69 2 2.0 4 F R 18 29 70 2 2.0 4 F R 20 32 71 2 2.4 4 F R 25 36 72 2 3.0 6 R R 18 27 73 2 3.0 6 R R 16 26 74 2 3.6 6 R R 18 27 75 2 6.2 8 R P 12 18 76 2 6.2 8 R P 14 19 77 2 3.0 6 A R 18 26 78 2 1.4 4 F R 26 38 79 2 1.4 4 F R 26 38 80 2 1.8 4 F R 22 35 81 2 1.8 4 F R 25 36 82 2 1.4 4 F R 26 39 83 2 1.4 4 F R 28 42 84 2 2.4 4 F R 22 33 85 2 2.4 4 F R 22 33 86 2 3.6 6 F R 17 26 87 2 2.4 4 F R 21 30 88 2 2.4 4 F R 20 31 89 2 3.6 6 F R 19 29 90 2 2.4 4 F R 21 30 91 2 2.4 4 F R 20 31 92 2 3.6 6 F R 19 29 93 2 6.4 8 R P 14 23 94 2 3.5 6 A R 17 25 95 2 2.5 4 F R 23 33 96 2 2.5 4 F R 22 30 97 2 2.5 4 F R 22 29 98 2 3.5 6 F R 18 27 99 2 3.0 6 F R 20 28 100 2 2.5 4 F R 41 36 101 2 2.5 4 F R 22 32 102 2 1.8 4 F R 29 40 103 2 1.8 4 F R 29 40 104 2 3.5 6 R P 27 32 105 2 3.7 6 F P 18 26 106 2 3.7 6 A P 17 24 107 2 5.6 8 R P 16 24 108 2 5.6 8 A P 16 23 109 2 3.5 6 A R 17 25 110 2 3.5 6 F R 18 27 111 2 2.5 4 F R 41 36 112 2 2.5 4 F R 22 31 113 2 2.5 4 F R 21 30 114 2 3.7 6 F R 18 27 115 2 2.3 4 F P 18 25 116 2 2.5 4 F R 23 32 117 2 3.5 6 F R 20 27 118 2 2.0 4 F R 27 34 119 2 2.0 4 F R 24 31 120 2 2.5 4 F R 24 30 121 2 2.5 4 F P 21 28 122 2 2.0 4 F R 18 28 123 2 2.0 4 F R 20 33 124 2 3.0 6 A R 18 26 125 2 3.2 6 F R 20 29 126 3 4.2 8 A P 18 28 127 3 6.3 12 A P 14 21 128 3 3.0 6 R P 17 25 129 3 3.0 6 R P 17 25 130 3 4.4 8 R P 15 22 131 3 4.4 8 A P 14 20 132 3 4.4 8 R P 14 22 133 3 4.4 8 A P 14 20 134 3 4.4 8 R P 14 22 135 3 4.4 8 A P 14 20 136 3 4.4 8 R P 14 22 137 3 4.4 8 A P 14 20 138 3 3.6 6 F R 18 30 139 3 3.6 6 F R 18 30 140 3 5.0 8 R P 15 23 141 3 3.8 6 R R 19 29 142 3 4.6 8 R P 17 26 143 3 5.0 8 R P 17 26 144 3 5.0 8 R P 16 25 145 3 2.0 4 F R 22 34 146 3 2.4 4 F R 24 35 147 3 2.4 4 F R 24 35 148 3 6.7 12 R P 11 18 149 3 6.7 12 R P 11 18 The US Department of Energy's Fuel Economy Guide provides fuel efficiency data for cars. A portion of the data is shown at the bottom of this worksheet. a. Do these data represent experimental or observational data? Explain and justify your answer. b. Describe the population that is represented by this sample. Justify your answer. c. How many observations are in this data set? d. How many variables are in this data set? e. How many data values are in this data set? f. Which of the variable(s) are quantitative? g. Which variables are categorical? h. Give an example of a question that could be answered by using descriptive statistics with these data. i. One consultant for a car rental company said: "We should stop offering large cars, based on their low MPG. They are just a waste of fuel.". Explain if the consultant is justified in making the statement. Car Size (1=Compact, 2=Midsize, 3=Large) Displacement Cylinders Drive Fuel Type City MPG Hwy MPG 1 1 2.0 4 F P 22 30 2 1 2.0 4 A P 21 29 3 1 2.0 4 A P 21 31 4 1 3.0 6 A P 18 28 5 1 3.0 6 A P 18 27 6 1 6.0 12 A P 12 19 7 1 4.4 8 R P 16 24 8 1 4.4 8 R P 15 22 9 1 3.6 6 R R 19 30 10 1 3.6 6 R R 18 29 11 1 3.6 6 R R 17 28 12 1 6.2 8 R R 15 24 13 1 6.2 8 R R 16 24 14 1 2.4 4 F R 18 29 15 1 3.6 6 F R 19 29 16 1 2.0 4 F R 28 38 17 1 2.0 4 F R 27 37 18 1 2.0 4 F R 26 36 19 1 2.0 4 F R 28 40 20 1 1.8 4 F R 28 39 21 1 1.8 4 F R 28 36 22 1 2.4 4 F P 22 31 23 1 1.8 4 F R 29 41 24 1 1.5 4 F R 44 44 25 1 1.6 4 F R 30 40 26 1 1.6 4 F R 30 40 27 1 2.5 4 F R 22 29 28 1 2.5 4 F R 20 28 29 1 4.7 8 R P 17 25 30 1 6.7 12 R P 11 18 31 1 6.7 12 R P 11 18 32 1 2.0 4 F R 18 28 33 1 2.0 4 F R 20 33 34 1 2.0 4 A R 18 29 35 1 2.0 4 A R 20 30 36 1 2.0 4 F R 19 29 37 1 2.0 4 F R 20 33 38 1 2.5 4 F R 23 31 39 1 2.5 4 F R 23 31 40 1 2.0 4 F P 22 31 41 1 2.0 4 F P 21 31 42 1 3.6 6 A P 17 25 43 1 2.5 5 F R 24 31 44 1 2.5 5 F R 23 33 45 1 2.0 4 F P 24 33 46 1 2.0 4 F P 21 31 47 1 2.0 4 F R 23 29 48 1 2.0 4 F P 24 32 49 1 2.0 4 F R 24 34 50 1 2.0 4 F P 22 33 51 1 2.5 5 F R 24 31 52 1 2.5 5 F R 23 33 53 1 2.5 5 F R 21 30 54 1 2.5 5 F R 21 29 55 1 3.0 6 A R 18 26 56 1 2.5 5 F R 20 30 57 2 3.5 6 F P 20 29 58 2 3.7 6 A P 18 26 59 2 3.7 6 A P 17 25 60 2 2.0 4 F P 25 33 61 2 2.0 4 F P 25 33 62 2 3.0 6 A P 19 28 63 2 3.0 6 A P 18 28 64 2 4.2 8 A P 18 28 65 2 6.0 12 A P 11 19 66 2 2.4 4 F R 25 36 67 2 3.6 6 F R 17 27 68 2 3.6 6 A R 16 26 69 2 2.0 4 F R 18 29 70 2 2.0 4 F R 20 32 71 2 2.4 4 F R 25 36 72 2 3.0 6 R R 18 27 73 2 3.0 6 R R 16 26 74 2 3.6 6 R R 18 27 75 2 6.2 8 R P 12 18 76 2 6.2 8 R P 14 19 77 2 3.0 6 A R 18 26 78 2 1.4 4 F R 26 38 79 2 1.4 4 F R 26 38 80 2 1.8 4 F R 22 35 81 2 1.8 4 F R 25 36 82 2 1.4 4 F R 26 39 83 2 1.4 4 F R 28 42 84 2 2.4 4 F R 22 33 85 2 2.4 4 F R 22 33 86 2 3.6 6 F R 17 26 87 2 2.4 4 F R 21 30 88 2 2.4 4 F R 20 31 89 2 3.6 6 F R 19 29 90 2 2.4 4 F R 21 30 91 2 2.4 4 F R 20 31 92 2 3.6 6 F R 19 29 93 2 6.4 8 R P 14 23 94 2 3.5 6 A R 17 25 95 2 2.5 4 F R 23 33 96 2 2.5 4 F R 22 30 97 2 2.5 4 F R 22 29 98 2 3.5 6 F R 18 27 99 2 3.0 6 F R 20 28 100 2 2.5 4 F R 41 36 101 2 2.5 4 F R 22 32 102 2 1.8 4 F R 29 40 103 2 1.8 4 F R 29 40 104 2 3.5 6 R P 27 32 105 2 3.7 6 F P 18 26 106 2 3.7 6 A P 17 24 107 2 5.6 8 R P 16 24 108 2 5.6 8 A P 16 23 109 2 3.5 6 A R 17 25 110 2 3.5 6 F R 18 27 111 2 2.5 4 F R 41 36 112 2 2.5 4 F R 22 31 113 2 2.5 4 F R 21 30 114 2 3.7 6 F R 18 27 115 2 2.3 4 F P 18 25 116 2 2.5 4 F R 23 32 117 2 3.5 6 F R 20 27 118 2 2.0 4 F R 27 34 119 2 2.0 4 F R 24 31 120 2 2.5 4 F R 24 30 121 2 2.5 4 F P 21 28 122 2 2.0 4 F R 18 28 123 2 2.0 4 F R 20 33 124 2 3.0 6 A R 18 26 125 2 3.2 6 F R 20 29 126 3 4.2 8 A P 18 28 127 3 6.3 12 A P 14 21 128 3 3.0 6 R P 17 25 129 3 3.0 6 R P 17 25 130 3 4.4 8 R P 15 22 131 3 4.4 8 A P 14 20 132 3 4.4 8 R P 14 22 133 3 4.4 8 A P 14 20 134 3 4.4 8 R P 14 22 135 3 4.4 8 A P 14 20 136 3 4.4 8 R P 14 22 137 3 4.4 8 A P 14 20 138 3 3.6 6 F R 18 30 139 3 3.6 6 F R 18 30 140 3 5.0 8 R P 15 23 141 3 3.8 6 R R 19 29 142 3 4.6 8 R P 17 26 143 3 5.0 8 R P 17 26 144 3 5.0 8 R P 16 25 145 3 2.0 4 F R 22 34 146 3 2.4 4 F R 24 35 147 3 2.4 4 F R 24 35 148 3 6.7 12 R P 11 18 149 3 6.7 12 R P 11 18

Explanation / Answer

Part (a) :   This is an observational data because this data was collected by observing the actual field performance of the various cars which are already running in operation. There was no deliberate attempt to collect the data by conducting experiments for cars with different distinct sets of characterising parameter values.

Part (b) : The population that is represented by this sample is the Set of all the cars which have been sold and are currently in operation, determined by all the possible values that the following 7-tuple parameter vector can take : (size, displacement, number of cylinders, drive type, fuel type, City MPG, Highway MPG) .

Part (c) : When we closely look at the data, we observe that total 132 distinct data records are there. Although the total count shown is 149, there are many record repeated more than once. So in this data set, there are total 132 observations.

Part (d) : There are total 7 variables in this data set namely 1.size, 2. displacement, 3. number of cylinders, 4.drive type, 5. fuel type, 6.city mpg , 7. highway mpg.

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