Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 20 stations last Tuesday, the correlation was .78. At the .01 significance level, is the correlation in the population greater than zero? (Round your answer to 3 decimal places.) The test statistic is . Decision: H0: 0 -------------------------------------------------------------------------------------------------------------The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year. Car 1 2 3 4 5 6 Age (years) 9 7 11 12 8 7 Selling Price ($000) 8.1 6.0 3.6 4.0 5.0 10.0 Car 7 8 9 10 11 12 Age (years) 8 11 10 12 6 6 Selling Price ($000) 7.6 8.0 8.0 6.0 8.6 8.0 Click here for the Excel Data File a. If we want to estimate selling price on the basis of the age of the car, which variable is the dependent variable and which is the independent variable? is the independent variable and is the dependent variable. b-1. Determine the correlation coefficient. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) X Y ( )2 ( )2 ( )( ) 9.0 8.1 0.084 1.192 0.007 1.420 0.099 7.0 6.0 -1.916 -0.908 3.674 0.825 1.741 11.0 3.6 2.083 -3.308 4.340 10.945 -6.892 12.0 4.0 3.083 -2.908 9.507 8.458 -8.967 8.0 5.0 -0.917 -1.908 0.840 3.642 1.749 7.0 10.0 -1.917 3.092 3.674 9.558 -5.926 8.0 7.6 -0.917 0.692 0.840 0.479 -0.634 11.0 8.0 2.083 1.092 4.340 1.192 2.274 10.0 8.0 1.083 1.092 1.174 1.192 1.18 12.0 6.0 3.083 -0.908 9.507 0.825 -2.80 6.0 6.0 8.6 8.0 -2.917 -2.917 1.692 1.092 8.507 8.507 2.862 1.192 -4.934 -3.184 107.000 82.900 = 8.916 54.917 = 6.908 sx = 42.590 sy = r= b-2. Determine the coefficient of determination. (Round your answer to 3 decimal places.) 0.296 c. Interpret the correlation coefficient. Does it surprise you that the correlation coefficient is negative? (Round your answer to nearest whole number.) correlation between age of car and selling price. So, % of the variation in the selling 30 price is explained by the variation in the age of the car. The production department of Celltronics International wants to explore the relationship between the number of employees who assemble a subassembly and the number produced. As an experiment, 2 employees were assigned to assemble the subassemblies. They produced 13 during a one-hour period. Then 4 employees assembled them. They produced 22 during a onehour period. The complete set of paired observations follows. Number of Assemblers 2 4 One-Hour Production (units) 13 22 -26.294 1 5 3 9 36 25 The dependent variable is production; that is, it is assumed that different levels of production result from a different number of employees. Click here for the Excel Data File b. A scatter diagram is provided below. Based on it, does there appear to be any relationship between the number of assemblers and production? , as the number of assemblers , so does the production. c. Compute the correlation coefficient. (Negative amounts should be indicated by a minus sign. Round sx, sy and r to 3 decimal places.) X Y 2 )2 ( 13 -1 -8 1 )2 ( 64 ( )( ) 8 4 22 1 9 5 36 3 25 15 1 1 1 -12 -2 2 4 sy = 3 10 = 21 r= sx = 24 225 0 15 105 = 144 4 4 0 1 1 16 450 30 0 63