Question: The Montgomery Athletic Shoe Company has developed a new shoe-sole material it thinks provides superior wear compared with the old material the company has been using for its running shoes. The company selected 10 cross-country runners and supplied each runner with a pair of shoes. Each pair had one sole made of the old material and the other made of the new material. The shoes were monitored until the soles wore out. The following lifetimes (in hours) were recorded for each material:
a. If the populations from which these samples were taken could be considered to have normal distributions, determine if the soles made of the new material have a longer mean lifetime than those made from the old material. Use a significance level of 0.025.
b. Suppose you were not willing to consider that the populations have normal distributions. Make the determination requested in part a.
c. Given only the information in this problem, which of the two procedures indicated in parts a and b would you choose to use? Give reasons for your answer.