10-3 Prediction Intervals and Variation 551 11. Predicting Highway Fuel Consumption Using a car weight of x = 4000 (pounds), what is the single value that is the best predicted amount of highway fuel consumption? 12. Finding a Prediction Interval For a car weighing 4000 pounds 1x = 40002, identify the 95% prediction interval estimate of the highway fuel consumption. Write a statement interpreting that interval. Finding a Prediction Interval. In Exercises 13–16, use the following paired data consisting of weights of large cars (pounds) and highway fuel consumption (mi , gal) from Data Set 35 “Car Data” in Appendix B. (These are the same data used in Exercises 9-12.) Let x represent the weight of the car and let y represent the corresponding highway fuel consumption. Use the given weight and the given confidence level to construct a prediction interval estimate of highway fuel consumption. Weight 3608 3962 4253 4006 3754 3859 3874 4674 4321 4346 3891 3957 Highway 32 27 25 31 28 30 30 24 27 26 33 31 13. Cars Use x = 3500 pounds with a 95% confidence level. 14. Cars Use x = 4200 pounds with a 99% confidence level. 15. Cars Use x = 3800 pounds with a 99% confidence level. 16. Cars Use x = 3750 pounds with a 95% confidence level. Variation and Prediction Intervals. In Exercises 17–20, find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. In each case, there is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. 17. Altitude and Temperature Listed below are altitudes (thousands of feet) and outside air temperatures (°F) recorded by the author during Delta Flight 1053 from New Orleans to Atlanta. For the prediction interval, use a 95% confidence level with the altitude of 6327 ft (or 6.327 thousand feet). Altitude (thousands of feet) 3 10 14 22 28 31 33 Temperature (°F) 57 37 24 -5 -30 -41 -54 18. Town Courts Listed below are amounts of court income and salaries paid to the town justices (based on data from the Poughkeepsie Journal). All amounts are in thousands of dollars, and all of the towns are in Dutchess County, New York. For the prediction interval, use a 99% confidence level with a court income of $800,000. Court Income 65 404 1567 1131 272 252 111 154 32 Justice Salary 30 44 92 56 46 61 25 26 18 19. Crickets and Temperature The table below lists numbers of cricket chirps in 1 minute and the temperature in °F. For the prediction interval, use 1000 chirps in 1 minute and use a 90% confidence level. Chirps in 1 min 882 1188 1104 864 1200 1032 960 900 Temperature 1 °F2 69.7 93.3 84.3 76.3 88.6 82.6 71.6 79.6 20. Weighing Seals with a Camera The table below lists overhead widths (cm) of seals measured from photographs and the weights (kg) of the seals (based on “Mass Estimation of Weddell Seals Using Techniques of Photogrammetry,” by R. Garrott of Montana State University). For the prediction interval, use a 99% confidence level with an overhead width of 9.0 cm. Overhead Width 7.2 7.4 9.8 9.4 8.8 8.4 Weight 116 154 245 202 200 191
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