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 decision should be made at the α = 0.05 level?

Because the P-value < α = 0.05, the correct decision is to reject H0.
Because the P-value < α = 0.05, the correct decision is to reject Ha.
Because the P-value < α = 0.05, the correct decision is to fail to reject H0.
Because the P-value < α = 0.05, the correct decision is to fail to reject Ha.

Answer 1

Because the P-value < α = 0.05, the correct decision is to reject H0.

Explanation:

When the p-value is less than our given significance level, it's outside the rejection region, so there is strong evidence that suggest the null hypothesis is not true and that the alternate hypothesis is favored instead.