A transportation department tests the braking abilities of various cars. For this experiment, the department measured the stopping distances on dry pavement at 100 kph (kilometers per hour, about 62 mph) of four models: A, B, C, and D. Each car accelerated to 100 kilometers per hour on a test track; then the brakes were applied. The distance required to come to a full stop was measured, in meters. The test was repeated for each car 10 times under identical conditions. The data are shown in the accompanying table. Complete parts (a) through (f). Click the icon to view the data table. ( Plot the data. From your visual inspection of the plot, do you think there are statistically significant differences among these four cars? Choose the correct graph below. O A. O B. O C. 50 50- Distance (m) Distance (m) Distance (m) 40- 40- ABC D 40- A BCD ABCD Car Model Car Model Car Model Are there any statistically significant differences among these four cars? O A. There appear to be large, consistent differences among the four cars. O B. There do not appear to be statistically significant differences among the four cars. O C. The outliers and large spread make it difficult to determine if there are statistically significant differences among the four cars. (b) Fit a multiple regression of stopping distance on three dummy variables that identify the cars A, C, and D. Interpret the estimated intercept and slopes. y = [+ ()D(A) + () D(C)+ ([)D(D) (Round to two decimal places as needed.) What do the estimated intercept and slope mean? A. The intercept is the average stopping distance of all the car models. The slopes represent the differences in the average stopping distance compared to the overall average stopping distance. O B. The intercept is the average stopping distance of car B. The slopes represent the differences in the average stopping distance compared to that of car B. O C. The intercept is the average stopping distance of car B. The slopes represent the average stopping distance for each corresponding car model.(c) Does a statistical test agree with your visual impression? Test the null hypothesis that the four cars have the same stopping distance. Use a = 0.05. What are the hypotheses for this test? O A. HO: HA # HB # HC # HD OB. HO: HA = HB = HC = HD Ha : HA = HB = HC = HD Ha : HA * HB # HC # HD O C. HO: HA = HB = HC = HD O D. Ho: At least one of the means is different. Ha: At least one of the means is different. Ha: HA = HB = HC = HD Find the F-statistic. F=(Round to the nearest integer as needed.) Find the p-value. p-value = (Round to three decimal places as needed.) What is the conclusion of the test for a = 0.05? O Since the p-value is greater than 0.05, do not reject Ho- O Since the p-value is greater than 0.05, reject Ho- O Since the p-value is less than 0.05, reject Ho- O Since the p-value is less than 0.05, do not reject Ho-(d) These stopping distances were recorded in meters. Would the analysis change had the distances been measured in feet instead? A. The estimates in the multiple regression (bo, b,, etc.) would increase by a factor of a bit more than 3, but the overall F-statistic and p-value would be the same. O B. All values in the analysis would increase by a factor of a bit more than 3. O C. The overall F-statistic and p-value would increase by a factor of a bit more than 3, but the estimates in the multiple regression (bo, b,, etc.) would be the same. O D. None of the values in the analysis would change. (e) Do these data meet the conditions required for an ANOVA? O A. No, because the errors are not independent. O B. No, because there are obvious lurking variables. O C. No, because there is no linear association between the data. O D. Yes, all the conditions are satisfied for an ANOVA. O E. No, because the residuals are not normal. O F. No, because the variances of the residuals are significantly different. (f) Based on these results, what should we conclude about differences in the stopping distance of other cars of these models? O A. The differences between the stopping distances of the four cars that were sampled are not statistically significant. O B. There are differences between the stopping distances of the four models that were sampled. O C. There are differences between the stopping distances of the four cars that were sampled, but nothing is known of other cars of the same models. O D. The data are not suitable for an ANOVA test.X Stopping distances Full data set Model Distance (meters) Model Distance (meters) A 44.4 42.8 A 45.2 43.4 A 45.2 42.9 A 45.5 43.5 A 45.6 42.4 A 45.5 43.4 45.3 42.7 44.4 43.6 44.4 43.3 45.8 42.8 47.8 47.8 49.6 49.0 49.2 45.6 48.2 47.1 49.5 47.5 48.8 48.0 48.5 47.0 48.5 47.9 48.2 48.4 48.3 47.8