Question

Researchers Hill and Barton used data from the 2004 Olympics to test whether one uniform color (red or blue) gave athletes a competitive advantage. In the sports of boxing tae kwon do, and wrestling, athletes are randomly assigned either a red or blue uniform. They found that out of 457 matches, the competitor in red won 248 times.

Let pi be the long-term probability that an Olympic match of boxing tae kwon do, or wrestling is won by the athlete wearing a red uniform. Then we want to test

H0:π=0.50

Ha:π≠0.50

a. Is a normal approximation for the null distribution appropriate?

A. No
B. Yes

b. Compute a theory-based p-value for this study. If a normal approximation is appropriate, then use a normal approximation. If not, then use a binomial distribution.

c. What is your conclusion?

A. There is moderate evidence that the long-term probability of winning for Olympic athletes in red uniforms is not 0.5.
B. There is strong evidence that the long-term probability of winning for Olympic athletes in red uniforms is not 0.5.
C. It is plausible that the long-term probability of winning for Olympic athletes in red uniforms is 0.5.

Answer 1

a) normal approximation is appropriate. because np =457 X 0.5>10

b) 0.0681

c) fail to reject null hypothesis.

d) C. It is plausible that the long-term probability of winning for Olympic athletes in red uniforms is 0.5.

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