Question

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.

Runner	Brand 1	Brand 2
1	31.23	32.02
2	29.33	28.98
3	30.50	30.63
4	32.20	32.67
5	33.08	32.95
6	31.52	31.53
7	30.68	30.83
8	31.05	31.10
9	33.00	33.12
10	29.67	29.50
11	30.55	30.57
12	32.12	32.20

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. Determine which of the following statements is TRUE.

We would not reject the null hypothesis of no difference at the 0.10 level.

We would reject the null hypothesis of no difference at the 0.10 level but not at the 0.05 level.

We would reject the null hypothesis of no difference at the 0.05 level but not at the 0.01 level.

We would reject the null hypothesis of no difference at the 0.01 level. Q. 2 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? The null hypothesis that the mean of the differences in running times (Brand 2 - Brand 1) is zero, versus the alternative hypothesis that this mean is greater than zero. The null hypothesis that p = 1/2, versus the alternative that p is not equal to 1/2, where p is the proportion of running times using Brand 1 that are faster than times using Brand 2. The null hypothesis that p = 1/2, versus the alternative that p > 1/2, where p is the proportion of running times using Brand 1 that are faster than times using Brand 2. The null hypothesis that M is zero, versus the alternative that M is not zero, where M is the median of running times for all runners who wore Brand 2 minus the running times for all runners who wore Brand 1

Answer 1

1)

option A is right.