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 chess-boxing. 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 null distribution shown. (Note this null distribution uses only 100 simulated samples and not the usual 1,000 or more.) 

Suppose you are testing the hypothesis H₀: π = 0.50 versus H_a: π > 0.50. 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. 

b. Keeping the sample size the same, you take a new sample and find a sample proportion of 0.55. 

c. With your original sample, you decided to test a two-sided alternative instead of H_a: π > 0.50.

Transcribed Image Text:

Probability of success (m): 0.5 Sample size (n): 20 Number of samples: 100 Animate: [ Draw Samples Total = 100 18 12 6 0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 Proportion of successes