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
finished 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. The 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.