Download Introduction to Chance Models (Section 1.1) Introduction A key step

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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: 𝜋 = 0.5 versus Ha: 𝜋 > 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: 𝜋 = 0.5 versus Ha: 𝜋 ≠0.5. What is your p-value now based
on the above null distribution?
5. Suppose you are testing the hypotheses H0: 𝜋 = 0.5 versus Ha: 𝜋 > 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: 𝜋 >
0.5.
LARGER
June 27, 2014
SMALLER
MAA PREP workshop
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