In this exploration, we are going to explore three factors that influence the strength of evidence in a test of significance: (1) the difference between the observed sample statistic and the value of the parameter used in the null hypothesis; (2) the sample size; and (3) one-sided tests versus two-sided tests. To do we will look at a study conducted by Hill and Barton (Nature, 2005) to investigate whether Olympic athletes in certain uniform colors have an advantage over their competitors. They noticed that competitors in the combat sports of boxing, tae kwon do, Greco-Roman wrestling, and freestyle wrestling are randomly assigned red or blue uniforms. For each match in the 2004 Olympics, they recorded the uniform color of the winner.

1. tate the null and the alternative hypotheses in words.
2. We will let
4. represent the probability that a competitor wearing a red uniform wins. Using this, restate the hypotheses using symbols.
5. Researchers Hill and Barton used data collected on the results of 457 matches and found that the competitor wearing red won 248 times, whereas the competitor wearing blue won 209 times. We will carry out a simulation to assess whether or not the observed data provide evidence in support of the research conjecture. This simulation will employ the3S strategy: Determine thestatistic,simulate could-have-been outcomes of the statistic under the null model, and assess thestrength of evidence against the null model by estimating the p-value or the standardized statistic.
6. What is the statistic we will use? Calculate the observed value of the statistic in this study.
7. Describe how you could use a coin to develop a null distribution to test our hypothesis.
8. Use theOne Proportionapplet to test our hypothesis. Based on your simulation, find the p-value and write conclusion. Also write down the mean and standard deviation from your null distribution when the proportion of successes is used for the variable on the horizontal axis. You will need this later.