Distance (km) At the end of an experiment, you often need to make a judgment about...

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Distance (km) At the end of an experiment, you often need to make a judgment about the reliability of a fit to an entire set of data. In particular, you often need to determine the uncertainty in a fitting parameter, such as a slope. In this exercise, imagine that you are testing the fuel efficiency of a new vehicle. You have hired four outside contractors to do measurements of how far the vehicle can drive with different amounts of fuel. They have all gathered data somewhat differently and you have to judge which one of the contractors can give you the most reliable measurement of fuel efficiency. The slope of the best fit in each graph is the fuel efficiency in units of km/litre and all of the fits have come very close to 50 km/litre. Your task is to invent a formula that can be applied to these four data sets in order to determine the uncertainty in this slope. Note that the model is a straight line going through the origin: Distance = 50 * (Fuel Consumption), so m = (50 8m) km/litre. The ultimate goal here is to determine the uncertainty in the slope. Distance (km) Contractor A 700.0 600.0 y = 50.0x 500.0 400.0 300.0 200.0 100.0 0.0 0.0 5.0 Fuel (L) 11111 Contractor B 700.0 600.0 y = 50.0x 500.0 Fuel (L) Distance (km) SD (km) Fuel (L) Distance (km) D (km) 8.0 379.6 Distance (km) 400.0 300.0 50.0 1.5 54.6 50.0 200.0 9.0 415.7 50.0 2.5 90.7 50.0 100.0 10.0 448.5 50.0 3.5 112.5 50.0 10.5 581.2 50.0 4.0 250.2 50.0 0.0 10.0 15.0 0.0 5.0 10.0 15.0 12.0 599.9 50.0 5.5 274.9 50.0 Fuel (L) 13.0 680.7 50.0 6.5 345.7 50.0 Fuel (L) Distance (km) SD (km) Fuel (L) Distance (km) D (km) Contractor C 0.5 79.3 50.0 1.5 47.5 50.0 Contractor D 1.5 52.6 50.0 2.5 192.3 50.0 700.0 600.0 y = 50.0x 500.0 2.0 37.5 50.0 3.5 137.8 50.0 700.0 2.5 90.7 50.0 4.5 334.0 50.0 600.0 3.0 115.7 50.0 5.5 207.4 50.0 y = 50.0x 3.5 112.5 50.0 6.0 281.1 50.0 400.0 300.0 200.0 100.0 0.0 Lill 0.0 4.0 245.2 50.0 4.5 275.2 50.0 5.0 238.5 50.0 Distance (km) 500.0 400.0 300.0 200.0 5.5 274.9 50.0 6.0 310.7 50.0 100.0 6.5 345.7 50.0 0.0 5.0 10.0 15.0 0.0 5.0 10.0 15.0 Fuel (L) Fuel (L) Question 7 Contractor B or C? Why? Contractor B or D? Why? Which contractor do you think has done a better job of measuring the fuel efficiency of the vehicle (that is, which has a smaller uncertainty in the slope)? Contractor A or B? Why? Distance (km) At the end of an experiment, you often need to make a judgment about the reliability of a fit to an entire set of data. In particular, you often need to determine the uncertainty in a fitting parameter, such as a slope. In this exercise, imagine that you are testing the fuel efficiency of a new vehicle. You have hired four outside contractors to do measurements of how far the vehicle can drive with different amounts of fuel. They have all gathered data somewhat differently and you have to judge which one of the contractors can give you the most reliable measurement of fuel efficiency. The slope of the best fit in each graph is the fuel efficiency in units of km/litre and all of the fits have come very close to 50 km/litre. Your task is to invent a formula that can be applied to these four data sets in order to determine the uncertainty in this slope. Note that the model is a straight line going through the origin: Distance = 50 * (Fuel Consumption), so m = (50 8m) km/litre. The ultimate goal here is to determine the uncertainty in the slope. Distance (km) Contractor A 700.0 600.0 y = 50.0x 500.0 400.0 300.0 200.0 100.0 0.0 0.0 5.0 Fuel (L) 11111 Contractor B 700.0 600.0 y = 50.0x 500.0 Fuel (L) Distance (km) SD (km) Fuel (L) Distance (km) D (km) 8.0 379.6 Distance (km) 400.0 300.0 50.0 1.5 54.6 50.0 200.0 9.0 415.7 50.0 2.5 90.7 50.0 100.0 10.0 448.5 50.0 3.5 112.5 50.0 10.5 581.2 50.0 4.0 250.2 50.0 0.0 10.0 15.0 0.0 5.0 10.0 15.0 12.0 599.9 50.0 5.5 274.9 50.0 Fuel (L) 13.0 680.7 50.0 6.5 345.7 50.0 Fuel (L) Distance (km) SD (km) Fuel (L) Distance (km) D (km) Contractor C 0.5 79.3 50.0 1.5 47.5 50.0 Contractor D 1.5 52.6 50.0 2.5 192.3 50.0 700.0 600.0 y = 50.0x 500.0 2.0 37.5 50.0 3.5 137.8 50.0 700.0 2.5 90.7 50.0 4.5 334.0 50.0 600.0 3.0 115.7 50.0 5.5 207.4 50.0 y = 50.0x 3.5 112.5 50.0 6.0 281.1 50.0 400.0 300.0 200.0 100.0 0.0 Lill 0.0 4.0 245.2 50.0 4.5 275.2 50.0 5.0 238.5 50.0 Distance (km) 500.0 400.0 300.0 200.0 5.5 274.9 50.0 6.0 310.7 50.0 100.0 6.5 345.7 50.0 0.0 5.0 10.0 15.0 0.0 5.0 10.0 15.0 Fuel (L) Fuel (L) Question 7 Contractor B or C? Why? Contractor B or D? Why? Which contractor do you think has done a better job of measuring the fuel efficiency of the vehicle (that is, which has a smaller uncertainty in the slope)? Contractor A or B? Why?