Question

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 1

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.

Step-by-step 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.