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Do wearing custom-made shoes, made specifically for the runner, help a runner run faster?

To answer this question, twelve competitive runners were randomly selected, and their maximum velocity (in mph) was recorded while wearing the custom-made shoes and then again while not wearing the custom-made shoes. (A time for rest was granted, and it was randomly determined if they ran with the custom-made shoes first or second. The runners ran 100 yards.)

State the null and alternative hypotheses for this problem.

Answer :

Final answer:

The null hypothesis (H0) states there is no difference in maximum velocity between custom-made and regular shoes, while the alternative hypothesis (H1) states that custom-made shoes result in a greater maximum velocity.

Explanation:

To determine if custom-made shoes help a runner run faster, we would establish the null and alternative hypotheses based on the recorded maximum velocity of runners with and without the custom-made shoes. The null hypothesis (H0) is typically a statement of no effect or no difference, so in this case, it would state that there is no difference in the maximum velocity of runners when they wear custom-made shoes compared to when they do not. Conversely, the alternative hypothesis (H1) suggests that there is an effect, implying the custom-made shoes do have an impact on the runners' maximum velocity.

Hence:

  • H0: μ_custom = μ_regular - The maximum velocity is the same with custom-made shoes as with regular shoes.
  • H1: μ_custom > μ_regular - The maximum velocity with custom-made shoes is greater than with regular shoes.

Where μ_custom refers to the average maximum velocity with custom-made shoes and μ_regular refers to the average maximum velocity with regular shoes.

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Rewritten by : Barada