14.73 [EX14-73] Track coaches, runners, and fans talk a lot about the “speed of the track.” The surface of the track is believed to have a direct effect on the amount of time that it takes a runner to cover the required distance. To test this effect, 10 runners were asked to run a 220-yard sprint on each of two tracks. Track A is a cinder track, and track B is made of a new synthetic material. The running times (in seconds) are given in the following table. Test the claim that the surface on track B is conducive to faster running times.

a. State the null and alternative hypotheses being tested. Complete the test using 0.05.

b. State your conclusions.

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Runner Track 1 2 3 4 56 7 8 9 10 A 27.7 26.8 27.0 25.5 26.6 27.4 27.2 27.4 25.8 25.1 B 27.0 26.7 25.3 26.0 26.1 25.3 26.7 27.1 24.8 27.1