Twelve runners are asked to run a 10kilometer race on each o

Twelve runners are asked to run a 10-kilometer race on each of 2 consecutive weeks. In one of the races, the runners wear one brand of shoe and in the other, a different brand. The brand of shoe they wear in each race is determined at random. All runners are timed and are asked to run their best in each race. The results (in minutes) are given below. Use the sign test for matched pairs to determine if there is evidence that times using Brand 1 tend to be faster than times using Brand 2. What are the hypotheses we wish to test?

Solution

The hypotheses are:

H0:p=1/2 vs Ha:p1/2 where p= the proportion of running times using Brand 1 that are faster than times using brand 2.