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QUESTION

Suppose two brothers named Mario and Luigi like to compete by playing a certain video game. Mario thinks he is better at this game than Luigi and...

Suppose two brothers named Mario and Luigi like

to compete by playing a certain video game. Mario thinks he

is better at this game than Luigi and sets out to prove it by

keeping track of who wins. After playing the game 30 times,

Mario won 18 of them (or 60%). Mario then declares that

this proves he is obviously the better player. Luigi, who just

fi nished Chapter 1 in his statistics class, realizes that perhaps

he and his brother are evenly matched and just by chance

Mario won 60% of the last 30 games. Luigi is going to test

this by running a test of significance.

a. Describe what the parameter is that Luigi should be testing.

b. State the appropriate null and alternative hypotheses in

the context of this study. (Hint: Luigi likes two-sided tests

because he knows that will make it harder to get strong

evidence that his brother is better.)

c. Using an appropriate applet, fi nd the p-value using

a theory-based test (one-proportion z-test; normal

approximation).

d. Summarize your conclusion from your p-value.

e. Th e p-value you found in part (c) should have been

greater than 0.05. Suppose the two brothers continue to

compete and Mario continues to win 60% of the games.

How many games will they have to play until he gets a

p-value less than 0.05 aft er retesting?

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