Question 9 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
A carnival game is designed so that approximately 10% of players will win a large prize. If there is evidence that the percentage differs significantly from this target, then adjustments will be made to the game. To investigate, a random sample of 100 players is selected from the large population of all players. Of these players, 19 win a large prize. The question of interest is whether the data provide convincing evidence that the true proportion of players who win this game differs from 0.10. What are the appropriate hypotheses for this test?
Answer
A
H0: p = 0.1 versus Ha: p ≠ 0.1, where p = the proportion of players who did win this game.
B
H0: p = 0.1 versus Ha: p > 0.1, where p = the proportion of players who did win this game.
C
H0: p = 0.1 versus Ha: p > 0.1, where p = the proportion of players who win this game.
D
H0: p = 0.1 versus Ha: p ≠ 0.1, where p = the proportion of players who win this game.
Explanation
Let p represent the true proportion of all players who win a large prize. The target rate is 0.10, so the null hypothesis is H₀: p = 0.10; because the question asks whether the rate differs in either direction, the alternative is Hₐ: p ≠ 0.10. Choice D correctly defines p as the proportion of players who win the game, rather than the observed sample proportion.
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