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4. You have heard that in sports like boxing there might be some competitive advantage to those wearing red uniforms. You want to test this with your new favorite sport of chessboxing. You randomly assign blue and red uniforms to contestants in 20 matches and find that those wearing red won 14 times (or 70%). You conduct a test of significance using simulation and get the following null distribution. (Note this null distribution uses only 100 simulated samples and not the usual 1000 or more.) a) Suppose you want to see if competitors wearing red win more than 50% of the matches in the long run, so you test H0: ð = 0.5 versus Ha: ð > 0.5. What is your p-value based on the above null distribution? b) Suppose you now want to see if competitors wearing either red or blue have an advantage, so you test H0: ð = 0.5 versus Ha: ð â 0.5. What is your p-value now based on the above null distribution? 5. Suppose you are testing the hypotheses H0: ð = 0.5 versus Ha: ð > 0.5. You get a sample proportion of 0.54 and find that your p-value is 0.08. Now suppose you redid your study with each of the following changes, will your new p-value be larger or smaller than the 0.08 your first obtained? a) You increase the sample size and still find a sample proportion of 0.54. LARGER SMALLER b) Keeping the sample size the same, you take a new sample and find a sample proportion of 0.55. LARGER SMALLER c) With your original sample, you decided to test a two-sided alternative instead of Ha: ð > 0.5. LARGER June 27, 2014 SMALLER MAA PREP workshop 46