Is it advantageous to wear the color red in a sporting contest? According to Hill and Ba...

Is it advantageous to wear the color red in a sporting contest? According to Hill and Barton (2005):

Although other colours are also present in animal displays, it is specifically the presence and intensity of red coloration that correlates with male dominance and testosterone levels. In humans, anger is associated with a reddening of the skin due to increased blood flow, whereas fear is associated with increased pallor in similarly threatening situations. Hence, increased redness during aggressive interactions may reflect relative dominance.

Because artificial stimuli can exploit innate responses to natural stimuli, we tested whether wearing red might influence the outcome of physical contests in humans. In the 2004 Olympic Games, contestants in four combat sports (boxing, tae kwon do, Greco-Roman wrestling, and freestyle wrestling) were randomly assigned red or blue outfits (or body protectors). If colour has no effect on the outcome of contests, the number of winners wearing red should be statistically indistinguishable from the number of winners wearing blue.

They thus tabulated the colors worn by the winners in these contests:

c. Are either of these hypothesis tests equivalent to that which would test the null hypothesis π_R = 1/ 2 versus the alternative hypothesis π_R = 1/ 2 , using as data the total numbers of wins summed over all the sports?

d. Is there any evidence that wearing red is more favorable in some of the sports than others?

e. From an analysis of the points scored by winners and losers, Hill and Barton concluded that color had the greatest effect in close contests. Data on the points of each match are contained in the file red-blue.xls. Analyze this data and see whether you agree with their conclusion.