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Rock-Paper-Scissors

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The table below shows the choices made by 128 players on the first turn of a Rock-Paper-Scissors game. Recall that rock beats scissors which beats paper which beats rock. A player gains an advantage in playing this game if there is evidence that the choices made on the first turn are not equally distributed among the three options. Use a goodness-of-fit test to see if there is evidence that any of the proportions are different from 1/3.

Option Selected Frequency
Rock 67
Paper 44
Scissors 17
Total 128

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Solution Summary

Each step of the procedure is explained. A table showing step-by-step calculations is given in the pdf file.

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Step 1) State the hypotheses.

H0: p1 = p2 = p3 = 1/3
H1: At least one of the probabilities above is different from 1/3

Step 2) Use the significance level 0.05 to find the Critical Chi-square value. ...

Solution provided by:
J Pye, MSc
Education
  • MSc, California State Polytechnic University, Pomona
  • MBA, University of California, Riverside
  • BSc, California State Polytechnic University, Pomona
  • BSc, California State Polytechnic University, Pomona
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  • "Hello, thank you for your answer for my probability question. However, I think you interpreted the second and third question differently than was meant, as the assumption still stands that a person still independently ranks the n options first. The probability I am after is the probability that this independently determined ranking then is equal to one of the p fixed rankings. Similarly for the third question, where the x people choose their ranking independently, and then I want the probability that for x people this is equal to one particular ranking. I was wondering if you could help me with this. "
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