834 CHAPTER 12 Statistics c) Determine the equation of the line of best fit for the commuting distance and the commuting time. y x 1.58 2.91 = + d) Use the equation in part (c) to estimate the commuting time, to the nearest minute, for a worker traveling 10 miles. 19 minutes 36. Sales The following table shows the average (mean) number of clients per month and the sales volume, in thousands of dollars, for 8 salespeople. Ian Allenden/Shutterstock $ DS Average number of clients 12 14 16 20 23 46 50 48 Sales (thousands $) 16 25 30 30 75 82 100 90 a) Determine the correlation coefficient between the average number of clients and the sales. 0.927 b) Determine whether a correlation exists at 0.05. α= Yes c) Determine the equation of the line of best fit for the average number of clients and the sales. y x 1.91 1.25 = + d) Use the equation in part (c) to estimate the sales for a person with an average number of clients per month of 25. $49,000 37. Selling Cups of Hot Chocolate The high temperature for seven January days in Chicago along with the number of cups of hot chocolate sold for those days at the C and C Coffee Shop are shown in the table below. DS High temperature ( F) ° 42 38 20 30 28 35 17 Cups of hot chocolate sold 35 45 60 52 55 47 65 a) Determine the correlation coefficient between the high temperature and the number of cups of hot chocolate sold. 0.979 − b) Determine whether a correlation exists at 0.01. α= Yes c) Determine the equation of the line of best fit for the high temperature and number of cups of hot chocolate sold. y x 1.07 83.30 = − + d) Use the equation in part (c) to estimate the number of cups of hot chocolate sold if the daily high temperature is 33 °F. ≈48 cups 38. Fuel Efficiency of Cars The following table shows the weights, in hundreds of pounds, for six selected cars. Also shown is the corresponding fuel efficiency, in miles per gallon (mpg), for the car in city driving. DS Weight (hundreds of pounds) 27 31 35 32 30 30 Fuel efficiency (mpg) 23 22 20 21 24 22 a) Determine the correlation coefficient between the weight of a car and the fuel efficiency. 0.804 − b) Determine whether a correlation exists at 0.01. α= No c) Determine the equation of the line of best fit for the weight of a car and the fuel efficiency of a car. y x 0.43 35.28 = − + d) Use the equation in part (c) to estimate the fuel efficiency of a car that weighs 33 hundred pounds. 21.1 mpg 39. Tips The following table shows the amount of a dinner bill and the amount of money left as a tip for 6 customers at a restaurant. DS $ Bill ($) 35.20 22.93 16.45 45.82 54.16 39.70 Tip ($) 5.50 4.50 2.00 9.00 10.00 5.75 a) Determine the correlation coefficient between the amount of a dinner bill and the amount of money left as a tip. 0.961 b) Determine whether a correlation exists at 0.05. α= Yes c) Determine the equation of the line of best fit for the amount of a dinner bill and the amount of money left as a tip. y x 0.20 1.05 = − d) Use the equation in part (c) to estimate the amount of money left as a tip by a customer with a dinner bill of $25.00. $3.95 40. Blood Pressure The following table shows the systolic blood pressure and diastolic blood pressure readings for six adults. DS Systolic 110 153 120 143 100 112 Diastolic 70 110 80 98 70 75 a) Determine the correlation coefficient between the systolic blood pressure and the diastolic blood pressure readings. 0.984 b) Determine whether a correlation exists at 0.05. α= Yes c) Determine the equation of the line of best fit for the systolic blood pressure and the diastolic blood pressure readings. y x 0.79 12.98 = − d) Use the equation in part (c) to estimate the diastolic blood pressure for an adult with a systolic blood pressure reading of 115. ≈78
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