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. The computer output gives the results of a z-test for one proportion. Test and CI for One Proportion Test of p = 0.1 vs p ≠ 0.1 Sample 1 X 19 N 100 Sample p 0.19 95% CI (0.113, 0.267) Z-Value 3.00 P-value 0.0027 What conclusion should be made at the a = 0.05 level? A) Because the P-value < a = 0.05, there is convincing evidence that the true proportion of players who win this game differs from 0.10. B) Because the P-value < a = 0.05, there is convincing evidence that the true proportion of players who win this game differs from 0.19. C) Because the P-value < a = 0.05, there is not convincing evidence that the true proportion of players who win this game differs from 0.10. D) Because the P-value < a = 0.05, there is not convincing evidence that the true proportion of players who win this game differs from 0.19.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section: Chapter Questions

Problem 8SGR

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Question

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. The computer output gives the results of a z-test for one proportion.

Test and CI for One Proportion

Test of p = 0.1 vs p ≠ 0.1

Sample
1

X
19

N
100

Sample p
0.19

95% CI
(0.113, 0.267)

Z-Value
3.00

P-value
0.0027

What conclusion should be made at the a = 0.05 level?

A) Because the P-value < a = 0.05, there is convincing evidence that the true proportion of players who win this game differs from 0.10.

B) Because the P-value < a = 0.05, there is convincing evidence that the true proportion of players who win this game differs from 0.19.