Question

1. 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 probability that is different from 1/3.

a) Identify the parameter in the question. (hint: the long-run proportion of …) (1 pts)

b) State the null hypothesis in words. (1 pts)

The null would be a player that starts with scissors is 33%

c) State the null hypothesis using symbols. (0.5 pts)

H_O π=33%

d) State the alternative hypothesis in words. (1 pts)

The alternative would be a player that has scissors wouldn’t be 33%

e) State the alternative hypothesis in symbols. (0.5 pts)

H_a  π≠33%

f) What is the value for the statistics? (1 pts) Assign a symbol to this value. (0.5 pts)

z=-4.9

g) Using an “one proportion” applet, find the p-value. Report your p-value here: ___0____

(1 pts)

h) Based on this p-value, do we have strong evidence against the null hypothesis?  (1 pts)

Yes.

i) Summarize the conclusion in the context of the problem. (1 pts)

Answer 1

where the researchers had 119 people play rock-paper-scissors against a computer. n= 119

They found 66 players (55.5%) started with rock,

39 (32.8%) started with paper,

and 14 (11.8%) started with scissors.

x=14 and phat = x / n = 14 / 119   = 0.1176

We want to see if players start with scissors with a probability that is different from 1/3.

a) Identify the parameter in the question. (hint: the long-run proportion of …)

b) State the null hypothesis in words.

The null would be a player that starts with scissors is 33%

c) State the null hypothesis using symbols.

H_O π=33%

d) State the alternative hypothesis in words.

The alternative would be a player that has scissors wouldn’t be 33%

e) State the alternative hypothesis in symbols.

H_a  π≠33% ( it is two tailed test)

f) What is the value for the statistics? (1 pts) Assign a symbol to this value.

z= -4.9    = (phat - p ) / SQRT((p*(1-p) / n)

g) Using an “one proportion” applet, find the p-value. Report your p-value here: the p value is < .00001.

h) Based on this p-value, do we have strong evidence against the null hypothesis?

Yes.

i) Summarize the conclusion in the context of the problem.

The alternative hypothesis accepted herer it would be a player that has scissors wouldn’t be 33%