For informal sports events, players often play "rock-paper-scissors" to decide who serves first or who is the home team etc. Two players simultaneously show one of the three objects. The player showing the dominant object (e.g., rock beats scissors) wins. The optimal strategy is to alternate among the three objects. Play the game rock/paper/scissors against the computer using the website:http://www.nytimes.com/interactive/science/rock-paper-scissors.html. Select the novice version of the computer to play against. Play for at least 30 rounds, but keep going for as long as you'd like. Keep track of which option you choose (rock or paper or scissors) for every round that you play (the computer will record this for you but that information will soon scroll off the screen, so make your own notes) Recall the "Rock-Paper-Scissors" scenario from Exercise 7. A friend conjectures that men are more likely to show rock than paper or scissors. To test this, you ask 50 male friends to play the game with you and you note the first choice of each male.

(a) State the appropriate hypotheses to be tested, in symbols and in words. (Pay particular attention to

whether this is a one-sided or a two-sided test.)

(b) Let the random variable X represent the number of males that show "rock" as their first choice. What

distribution does X follow if the null hypothesis is true? Explain.

(c) Suppose 23 men choose rock first. Determine the p-value from these data, and indicate whether the

null hypothesis would be rejected at any commonly used significance level.

(d) Use technology to determine a 95% confidence interval for the parameter. Interpret this interval,

including a clear statement of what the parameter is.

(e) Is the confidence interval consistent with your test result? Explain.