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.

Are the conditions for inference met for conducting a z-test for one proportion?

A) Yes, the random, 10%, and large counts conditions are all met.
B) No, the random condition is not met.
C) No, the 10% condition is not met.
D) No, the large counts condition is not met.

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Answer :

sheenuvt12 sheenuvt12 · Answer 1 · 2025-05-12T05:26:50-04:00

Yes, the random, 10%, and large counts conditions are all met.

Here, the expected count of players who win a large prize is

np = 100 x 0.10

np = 10

and, the expected count of players who do not win a large prize is

n(1-p) = 100 x 0.90 = 90.

The second prerequisite is also satisfied because both of these anticipated counts are higher than or equal to 10.

The independence criteria is also satisfied if each player's outcome is independent of the results of the other players.

Therefore, Yes, the random, 10%, and large counts conditions are all met.

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