In: Statistics and Probability
In Vienna, Eliud Kipchoge became the first athlete to run a
marathon in less than two hours. Kipchoge wore a special type of
shoe developed by Nike called Vaporfly that is different than all
previous running shoes. It has a much thicker midsole and has a
layer of carbon fiber to bounce back as much energy as possible.
Nike engineers claim that Vaporfly is significantly faster than any
other shoe. Specifically, they claim that Vaporfly improves
anybody’s running time by 4% compared to the company’s best running
shoes.
A) Design an experiment to validate Nike's claims of 4%
improvement.
B) Suppose you have running times for 1275 runners who completed
the Boston Marathon in 2017 and 2018. Of the 1,275 runners who run
Boston for both years 52 switched to Vaporflys in 2018. You have
compared 2018 vs 2017 running times for all 1275 athletes and it is
clear that most of those 52 runners who switched to Vaporflys have
faster times in 2018 compared to 2017. On average the persons who
switched to vaporflys improved their time by 5%. Do you conclude
that wearing Vaporfly makes you run faster or do you need
additional information to back Nike's assertion of 4% improvement?
If you do need additional information state what additional
calculations you need to do.