Question: Consider the experiment to compare consumer evaluation of the durability of two types of jogging shoes, A and B. Ten daily joggers were randomly selected for the experiment. Each were given one pair of each type of shoe, and the joggers were instructed to use one of the shoe types until, according to his or her evaluation, the shoe was no longer usable. The jogger then shifted to the other shoe type and repeated the experiment. The order of use of shoe type was randomly assigned for each jogger. The number of weeks of service for each type of shoe was recorded for each jogger. The resulting data, matched on joggers, is given in the following table:

(a) Do the data provide sufficient information to indicate that the mean length of usable service for shoe type A is different from the corresponding mean length for shoe type B? Test using ? = .05.

(b) Construct a 95% confidence interval for the mean difference.