Twelve Runners Are Asked to Run a 10-Kilometer Race on Each

Multiple Choice

Twelve runners are asked to run a 10-kilometer race on each of two 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?

A) H₀:  = 0 versus H_a:  > 0,where  = the mean of the differences in running times (Brand 2 - Brand 1) for all runners who run this race twice wearing the two brands of shoes
B) H₀: p = ¹/₂ versus H_a: p  ¹/₂,where p = the proportion of running times using Brand 1 that are faster than times using Brand 2
C) H₀: p = ¹/₂ versus H_a: p > ¹/₂,where p = the proportion of running times using Brand 1 that are faster than times using Brand 2
D) H₀: population median = 0 versus H_a: population median  0,where the median of the differences in running times for all runners who run this race twice wearing the two brands of shoes is measured for Brand 2 - Brand 1