A shoe designer wishes to test whether a new experimental de

A shoe designer wishes to test whether a new (experimental) design for running shows leads to increased performance over an existing (control) design. She samples 14 runners and has each person run a five mile course two times, once in each pair of shoes. She records the following running times (in minutes) for each person.

Suppose we conduct a sign test to test her hypothesis. If we start off assuming the null hypothesis is true, what is the value of P (the probability of running faster in the experimental show compared to the control show for any given person) that we would use for the binomial distribution that is used within the sign test?

Solution

the probability of running faster in the experimental show compared to the control show for any given person

P(x=X) = nCx * p^x * q^(n-x)