Question

1)

Rock-paper-scissors is a hand game played by two or more people where players choose to sign either rock',rock′,paper', or `scissors' with their hands. We would like to test if players choose between these three options randomly, or if certain options are favored above others. What hypothesis test should we conduct to answer this research question?

• Compare two means
• Compare two proportions
• Chi square test of goodness of fit
• Chi square test of independence

2)

6.43 Rock-paper-scissors: Rock-paper-scissors is a hand game played by two or more people where players choose to sign either rock, paper, or scissors with their hands. For your AP Statistics class project, you want to evaluate whether players choose between these three options randomly, or if certain options are favored above others. You ask two friends to play rock-paper-scissors and count the times each option is played. The following table summarizes the data:

Rock	Paper	Scissors
43	21	35

Use these data to evaluate whether players choose between these three options randomly, or if certain options are favored above others. Make sure to clearly outline each step of your analysis, and interpret your results in context of the data and the research question.
The hypotheses to test the research question are:

• Ho: p_rock = .43, p_paper = .21, p_scissors = .35
  Ha: at least one of the probabilities is different
• Ho: the distribution is uniform
  Ha: this distribution is not uniform
• Ho: people choose rock twice as much as paper
  Ha: paper is the best choice

The value of the test statistic is:  (please round to two decimal places) The degrees of freedom associated with this test are:  The p-value associated with this test is:  (please round to four decimal places) Discuss the conclusion of the test in the context of the research study:

• The data provide sufficient evidence to claim that rock, paper, and scissors are not chosen equally as often as one another
• The data do not provide sufficient evidence to claim that rock, paper, and scissors are not chosen equally as often as one another

Answer 1

1)

Chi square test of goodness of fit

2_)

Ho: the distribution is uniform
Ha: this distribution is not uniform

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1	0.33	43.00	33.00	1.74	3.030
2	0.33	21.00	33.00	-2.09	4.364
3	0.33	35.00	33.00	0.35	0.121
total	1.000	99	99		7.5152
test statistic X2 =	7.515

degree of freedom =categories-1=

2

p value =

0.0233

since p value <0.05

The data provide sufficient evidence to claim that rock, paper, and scissors are not chosen equally as often as one another