3. A consumer protection group compares three different types of front bumpers for a bi and of automobile A test is conducted by driving an automobile into a brick wall at 15 mules per hour. The response is the amount of damage to the car, as measured by the repair costs, in hundreds of dollars Due to the potentially large costs. the study conducts only two tests with each bumper type. Table 12.26 shows the results

a) Report the sample means for the three bumpers.

b) Find the within-groups sum of squares and the associated vanance estimate.

c) Find the between-groups sum of squares and its associated variance estimate

d) Test the hypothesis that the mean repair costs are the same for the three types of bumpers. Report the test statistic, df values, P-value, and interpret

e) Construct an ANOVA table for displaying the results of this analysis.

f) Construct a 95% confidence interval for the difference between the truc means for bum- pers A and B. Interpret. g) Construct simultaneous 94% confidence intervals for the differences in mean repain costs for cach pair of bumpers. Interpret the results. and provide a diagram that indicates which types of bumpers, if any, are judged to be different in mican repair cost h) Set up the regression model with dummy variables for these data Show the corre- spondence between the hypothesis for the means and the hypothesis for the regression parameters. Provide the prediction equation. TABLE 12.26 TABLE 12.27 Bumper A Bumper B Bumper C Group A Group B Group C 2 11 4 3 4 15 6 S 10 8 5