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(Exercises 27–40) For each description of data, identify the W’s, name the variables, specify for each variable whether its use indicates that it should be treated as categorical or quantitative, and, for any quantitative variable, identify the units in which it was measured (or note that they were not provided).
36. Fuel economy The Environmental Protection Agency (EPA) tracks fuel economy of automobiles based on information from the manufacturers (Ford, Toyota, etc.). Among the data the agency collects are the manufacturer, vehicle type (car, SUV, etc.), weight, horsepower, and gas mileage (mpg) for city and highway driving.
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- Oil ProductionThe following table shows the amount of crude oil in billions of barrels produced in the United States in recent years. Source: U.S. Energy Information Administration. Year Crude Oil Produced 2002 2.097 2003 2.060 2004 1.989 2005 1.893 2006 1.857 2007 1.853 2008 1.830 2009 1.954 2010 2.000 2011 2.063 2012 2.377 In this exercise we are interested in the total amount of crude oil produced over the 10-year period from mid-2002 to mid-2012, using the data for the 11 years above. One approach is to sum up the numbers in the second column, but only count half of the first and last numbers. Give the answer to this calculation. Approximate the amount of crude oil produced over the 10-year period 2002-2012 by taking the average of the left endpoint sum and the right endpoint sum. Explain why this is equivalent to the calculation done in part a. This is also equivalent to a formula known as the trapezoidal rule, discussed in the next chapter. If your calculator has a cubic regression feature, find the best-fitting cubic function for these data, letting t=0 correspond to 2000. Then integrate this equation over the interval [2.12] to estimate the amount of crude oil produced over this time period. Compare with your answer to part a.arrow_forwardRunning In 1987, Canadian Ben Johnson set a world record in the 100-m sprint.The record was later taken away when he was found to have used an anabolic steroid to enhance his performance. His speed at various times in the race is given in the following table . Source: Information Graphics. Timesec Speedmph 0 0 1.84 12.9 3.80 23.8 6.38 26.3 7.23 26.3 8.96 26.0 9.83 25.7 a. Use the information in the table and left endpoints to estimate the distance that Johnson ran in miles. You will first need to calculate t for each interval. At the end, you will need to divide by 3600 the number of seconds in an hour, since the speed is in miles per hour. b. Repeat part a, using right endpoints. c. Wait a minute, we know that the distance Johnson ran is 100m. Divide this by 1609, the number of meters in a mile, to find how far Johnson ran in miles. Is your answer from part a or part b closer to the true answer? Briefly explain why you think this answer should be more accurate. d.arrow_forward
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