Question

Have you ever played rock-paper-scissors (or Rochambeau)? It’s considered a "fair game" in that the two players are equally likely to win (like a coin toss). Both players simultaneously display one of three hand gestures (rock, paper, or scissors), and the objective is to display a gesture that defeats that of your opponent. The main gist is that rocks break scissors, scissors cut paper, and paper covers rock. We investigated some results of the game rock-paper-scissors, where the researchers had 119 people play rock-paper-scissors against a computer. They found 66 players (55.5%) started with rock, 39 (32.8%) started with paper, and 14 (11.8%) started with scissors. We want to see if players start with scissors with a long-term probability that is different from 1/3.​

Answer 1

Answer:

players start with scissors with long term probability that is different from 1/3.

Step-by-step explanation:

Total number of people played rock-paper-scissor= 119

66 players started with rock= 55.5%

39 people started with paper = 32.8%

14 players started with scissor = 11.8 %

Sample proportion =x= 11.8% = 0.118

Population mean = µ= 1/3 = 0.333

Sample size = n=119

We know that test statistic formula is :

Z = x-µ / √(∂/n)

By using the test statistics formula

And putting all values, we get

Z = (0.118 – 0.33)/ √(0.33(1-0.33)/119)

  = (0.212) / √(0.33(0.67)/119)

= (0.212) / √(0.2211/119)

= (0.212) / √0.00186

= (0.212) / 0.0431

z= 4.91

players start with scissors with long term probability that is different from 1/3.