Question

ock-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: people choose rock twice as much as paper
  Ha: paper is the best choice
• 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

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:

• greater than .1
• between .05 and .1
• between .01 and .05
• less than .01

Discuss the conclusion of the test in the context of the research study:

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

Answer 1

Rock - Rock - 43 Paper 21 Observed frequency 43 35 Scissors 35 33 Expected frequency - 33 33 3 = 9/8 = 33] © Ho : The distribution is uniform Hai The distribution is not uniform Test Statistic (x) a s observed – Expected) Expected (43-33)+(21-33+(35-33) (35-33 33 33 33 = 7.51515 ~ 7.52] © Degrees of freedom = 3-1= 2 p-value = P(x2 >7.51515) = 0.0233 The p-value associated with this test is: (between 0.01 and 0.05]

** For the conclusion part of the question, you need to provide the significance level (sigma) of the test. You can provide it on the comment section, I will respond you immediately. Thank you.