The Belmont Stakes is the last and longest of the three horse races that make up the Triple Crown. Curiously, some of the Belmont races have been run clockwise around the track, and others have been run counterclockwise. Do the horses care? Here are boxplots and a confidence interval for the difference in mean speeds (in miles per hour). (Data in Belmont Stakes 2015)

a) What conclusion can you draw?
b) But wait. Not only has the direction been inconsistent, but so has the length of the race (in miles).

Comment on what you see in this plot.
c) The most common, and the current, length of the race is 1.5 miles. So let’s restrict our attention to only the races of that length.

Do you expect a confidence interval for the difference in mean speeds based only on these races to be wider, narrower, or about the same as the interval found earlier?
d) There is, in fact, a lurking variable in these data. Using the data file Belmont Stakes 2015, identify the lurking variable and, if necessary, update your conclusion about the direction that racehorses prefer to run.

Transcribed Image Text:

Speed 37.50 36.25 35.00 33.75 32.50 。 HIHO Clockwise Counter-clockwise Direction