Question

1.5.18 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, 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 rock with a probability that is different from 1/3. Which of the following states the appropriate null and alternative hypotheses in the context of this study, first in words and then in symbols? Null: The long-run proportion of times that a player starts with rock is 50%. Alt: The long-run proportion of times that a player starts with rock is different from 50%. 'A' Null: The long-run proportion of times that a player starts with rock is 33%. Alt: The long-run proportion of times that a player starts with rock is different from 33%. Null: The long-run proportion of times that a player starts with rock is 33%. Alt: The long-run proportion of times that a player starts with rock is more than 33%. Null: The long-run proportion of times that a player starts with rock is 33%. Alt: The long-run proportion of times that a player starts with rock is less than 33%.

please give answer in a,b,c,d format. give calculation.

Answer 1

Ans:

1)

Hypothesis statements:

Null:The long run proportion of times that a player starts with rock is 33%.

Alt:The long run proportion of times that a player starts with rock is different from 33%

Option b is correct.

2)

sample proportion=0.555

Test statistic:

z=(0.555-0.33)/sqrt(0.33*(1-0.33)/119)

z=5.22

p-value(2 tailed)=2*P(z>5.22)=0.0000

We have very strong evidence that the long run proportion of times that a player starts with rock is different from 33%

Option b is correct.