Chapter 15, Problem 18CP

Comparing more bumpers Refer to the previous exercise.

1. a. Would the results of your analysis change if for the second Bumper A the repair cost was $9000 instead of $2500? What does this illustrate about the analysis?
2. b. Suppose the company actually wanted to compare three bumper types. Which significance test could it use to do this if it did not want to assume that the repair costs have a normal distribution for each bumper type?

15.17 Car bumper damage An automobile company compares two types of front bumper for its new model by driving sample cars into a concrete wall at 15 miles per hour. The response is the amount of damage to the car, as measured by the repair costs, in dollars. Due to the costs, the study uses only six cars, obtaining results for three bumpers of each type. The results are in the table.

1. a. Find the ranks and the mean rank for each bumper type.
2. b. Show that there are 20 possible allocations of ranks to the two bumper types.
3. c. Explain why the observed ranks for the two groups are one of the two most extreme ways the two groups can differ, for the 20 possible allocations of the ranks.
4. d. Explain why the P-value for the two-sided test equals 0.10.