In problem 9 in Chapter 17, we described a study demonstrating that the color red is often associated with male dominance. Hill and Barton (2005)

monitored the outcome of four combat sports (boxing, Tae Kwon Do, Greco-Roman wrestling, and freestyle wrestling) during the 2004 Olympic games and found that participants wearing red outfits won significantly more often than those wearing blue.

a. If athletes wearing red won 31 out of 50 matches, is that sufficient to be significantly more than would be expected by chance? Use a two-tailed test with α = .05.

b. If 62 out of 100 wearing red won, is that enough to be significant using a two-tailed test with α = .05.

c. Note that the percentage of winning for red uniforms in part a is identical to the percentage in part b (31/50 = 62/100 = 62%) however, one is significant and the other is not. Explain why the two samples lead to different conclusions.