Two brands of tires are being tested for tread wear. To
control for vehicle and driver variation, one tire of each brand is put on the
front wheels of 10 cars. The cars are driven under normal driving conditions
for a total of 15,000 miles. The tread wear is then measured using a very
sophisticated instrument. The data that were observed are in the file Tread
Wear. (Note that the larger the number, the less wear in the tread.)
a. What would be the possible objection in this case for
employing the paired-sample t-test? Discuss.
b. Assuming that the decision makers in this situation are
not willing to make the assumptions required to perform the paired-sample
t-test, what decision should be reached using the appropriate nonparametric
test if a significance level of 0.05 is used? Discuss.