Question

please do just # 2 and #3

1. Rock-Paper-Scissors, also called Roshambo, is a popular two-player game often used to quickly determine a winner and loser. In the game, each player puts out a fist(rock), a flat hand (paper), or a hand with two fingers extended (scissors). In the game, rock beats scissors which beats paper which beats rock. The question is: Are people more likely to pick rock ? Knowing the frequencies by which the options are selected would give a player a significant advantage. Suppose we are convinced that people choose rock more often than the other two. You want to perform a hypothesis test to support that someone is more likely to choose rock than the other two options. Suppose a study observed 300 people playing Rock-Paper-Scissors, Their choices for their first turn are shown below: Option Selected Frequency 165 96 39 300 Rock Paper Scissors Total (a) State the null and alternative hypothesis for testing the claim that individuals are more likely to pick rock than either paper or scissors. For the null hypothesis think about what happens if they are all equally likely to be picked. Make sure that you include (and define) a parameter in the null and alternative hypothesis. (b) We can simulate the null distribution using the rflip function in R just like we did for the tea tasting example. We can adjust the probability under the null to any probability (the default is 0.5). To do this include "prob-” in your argument. For example, rflip(300,prob-33) will do a simulation 300 times (300 flips of a coin) where the probability is 0.33 (imagine that the probability of a coin landing heads is 0.33) Adjust the Rcode that we used for the tea tasting example and compute the p-value for the above hypothesis test. Make sure to change the probability to suit this particular hypothesis test. Report the p-value

2. Repeat the steps in 1), however, test the claim that individuals are less likely to pick scissors than the other two options. Report the p-value and state a conclusion at the α = 0.05-level.Be sure to state the null and alternative hypotheses.

3. Approximately 10% of Americans are left-handed (we will treat this as a population parameter). A study on the relationship between handedness and profession found that in a random sample of 105 lawyers, 16 of them were left-handed. Do the data provide sufficient evidence that lawyers are more likely to be left-handed than the rest of the population. State the null and alternative hypothesis and report the p-value. State a conclusion in context of the problem

Answer 1

Solution. 3-

Appropriate hypotheses would be -

H₀ : p = 0.1

Ha : p > 0.1

Observed value of test statistic =

$\frac{\hat{p}-p}{\sqrt{\frac{\hat{p}*(1-\hat{p})}{n}}}$

where $\hat{p} =$ observed proportio of left handed lawyers = 16/105 = 0.15238 and n = 105

then after putting the values above we get,

test statistic = 1.4935

P-value is calculated as-

P(Z > 1.4935)

= 0.0676

as level of significance 5% is less than P- value then we can say that null hypothesis is not rejected at 5% level of significance.

And hence there is not sufficient evidence that lawyers are more likely to be left-handed than the rest of the population

TY!