An automobile company compares two types of front bumper for their 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.
a. Find the ranks and the mean rank for each bumper type.
b. Show that there are 20 possible allocations of ranks to the two bumper types.
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.
d. Explain why the P-value for the two-sided test equals 0.10.

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Bumper A Bumper 1100 1300 1400 2100 2500 2300