Question

At a significance level of 0.01, does the observed proportion of winning tickets in the sample of 50 support the lottery's claim that 10% of its tickets win prizes?

1.Reject the claim; the sample proportion significantly differs from 10%.
2.Fail to reject the claim; the sample proportion aligns with the 10% claim.
3.Insufficient evidence to decide whether to reject or fail to reject the claim.
4.Accept the claim; the sample proportion matches the expected 10%.

Answer 1

At a significance level of 0.01, we compare the observed proportion of winning tickets in the sample of 50 to the claimed proportion of 10% using a one-sample proportion z-test. If the p-value is less than 0.01, we reject the claim and conclude that the sample proportion significantly differs from 10%.

Step-by-step explanation:

To determine whether the observed proportion of winning tickets in the sample of 50 supports the lottery's claim that 10% of its tickets win prizes, a hypothesis test can be conducted. At a significance level of 0.01, we compare the sample proportion to the claimed proportion using a one-sample proportion z-test. If the p-value is less than 0.01, we reject the claim and conclude that the sample proportion significantly differs from 10%. Therefore, the correct answer is 1. Reject the claim; the sample proportion significantly differs from 10%.