Question

Twelve world-class 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 second brand. Which brand they wear in which 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	Diff
1	31.23	32.02	–0.79
2	29.33	28.98	0.35
3	30.50	30.63	–0.13
4	32.20	32.67	–0.47
5	33.08	32.95	0.13
6	31.52	31.53	–0.01
7	30.68	30.83	–0.15
8	31.05	31.10	–0.05
9	33.00	33.12	–0.12
10	29.67	29.50	0.17
11	30.55	30.57	–0.02
12	32.12	32.20	–0.08

We use the sign test for matched pairs to determine if there is evidence that times using brand 1 tend to be less than times using brand 2.

Reference: Ref 7-11

Suppose in a similar set of data used to conduct this hypothesis test the P-value is 0.043. If a significance level of 0.05 is used, we would conclude that there is:

	statistically significant evidence that there is not a difference in the runners' times for the two brands of shoes.
	statistically significant evidence that the times using brand 1 tend to be less than the times using brand 2.
	statistically significant evidence that the times using brand 2 tend to be less than the times using brand 1.
	no statistically significant evidence of a difference in times for the two brands of shoes.

Answer 1