The color red is often associated with anger and male dominance.Based on this observation,Hill and Barton(2005) monitored the outcome of 4 combat sports( Boxing,tae kwan do,Greco-Roman wrestling and free style wrestling) during 2004 Olympics games and found that participants wearing red outfits won significatly more often than those wearing blue.
A: In 50 wrestling matches involving red outfits won 31 times lost 19 times.Is this result sufficient to conclude that red wins more than would be expected?
B: In 100 matches,suppose red won 62 times and lost 38. Is this sufficent to conclude that red wins more than would be expected by chance? Again use Q=Population standard mean.
C: Note that the winning percentage for red uniforms in part a is identical to the percentage in part b(31 out of 50 is 62 %,and 62 out of 100 is also 62%).
Although the two samples have an identica winning percentage,one is significant and the other is not. Explain why the two samples lead to different conclusions.