A carnival game is designed so that approximately 10 percent 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 point 1 0 Are the conditions for inference met for conducting a z - test for one proportion?
Answer
A
Yes, the random, 10 percent , and large counts conditions are all met.
B
No, the random condition is not met.
C
No, the large counts condition is not met.
D
No, the 10 percent condition is not met.
Explanation
The sample was randomly selected, so the random condition is met. The population is large, so 100 players is less than 10% of it. For the large counts condition, use the target proportion under the null: 100(0.10) = 10 expected wins and 100(0.90) = 90 expected non-wins; both are at least 10. Therefore, all three conditions are met, as choice A states.
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