In the game of Rock-Paper-Scissors, Rock crushes Scissors (that is, Rock wins),

Question

In the game of Rock-Paper-Scissors, Rock crushes Scissors (that is, Rock wins), Scissors cuts Paper, and Paper covers Rock. Rock-Paper-Scissors is truly an international game. On a bus in any city of the world, without saying a word 2 passengers will spontaneously use Rock-Paper-Scissors to determine who gets the last unoccupied seat on the bus. Rock-Paper-Scissors championships are held annually in several countries. The game is not random, experienced players have sophisticated strategies. When competing against a male who is inexperienced at Rock-Paper-Scissors, it is generally thought that the best strategy is Paper since Rock is perceived as strong and forceful and so will be the first throw of most males. To test this theory, a study observed 119 males playing Rock-Paper-Scissors; their choices for the first "throw" are shown below: First throw Frequencies Rock 66 Paper 39 Scissors 14 Question 1. Use the data in the table to calculate a 95% confidence interval forp, the proportion of first throws by males that are Rock. Lower bound of confidence interval (use 3 decimal places) Upper bound of confidence interval (use 3 decimal places) Question 2, If we want to estimate the proportion of first "throws" by males that are Rock to within 0.05 with 98% confidence, how large of a sample do we need? Assume that Rock, Paper, and Scissors are equally likely on the first throw, that is, use p-. 3

Explanation / Answer

Solution1:

sample proprtion of first "throws: by males that are rock

=x/n=66/119=0.5546218

z crit for 95%=1.96

95% confidence interval for true proprtion of first "throws: by males that are rock

=p^-zsqrt(p^(1-p^)/n,p^+zsqrt(p^(1-p^)/n

=0.5546218-1.96*sqrt(0.5546218*(1-0.5546218)/119), 0.5546218+1.96*sqrt(0.5546218*(1-0.5546218)/119)

= 0.4653, 0.6439

0.465<p<0.644

lower limit=0.465

Upper limit=0.644

Solution2:

p=1/3

q=1-1/3=2/3

E=0.05

Z crit=2.326

required sample size=n

n=p(1-p)(Z crit/E)^2

=1/3*2/3*(2.326/0.05)^2

=2/9*(2.326/0.05)^2

=480.9

n=481

Required sample size=481

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