During the 2004 Olympic Games, Hill and Barton (2005) monitored contests in four combat sports: Greco-Roman wrestling, freestyle wrestling, boxing, and tae kwon do. Half of the competitors were assigned red outfits and half were assigned blue. The results indicate that participants wearing red won significantly more contests. Suppose that a sample of n = 100 contests produced 60 winners wearing red and only 40 wearing blue. a. Is this enough evidence to justify a conclusion that wearing red produces significantly more wins than would be expected by chance? Use a two-tailed test with α = .05.
b. Because the outcome of the binomial test is a borderline z-score, use the real limits for X = 60 to determine if the entire z-score interval is located in the critical region. If any part of the interval is not in the critical region, the correct decision is to fail to reject the null hypothesis.