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 second brand. The brand 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. Assume normality of the populations. Is there sufficient evidence that the mean time using brand 1 is different than the mean times using brand 2? 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 32.30