Question

(round to three decimal places as needed. use a comma to separate answers as needed.) choose the correct conclusion below. a. fail to reject h₀. there is enough evidence at the 1% level of significance to support the claim b. reject h₀. there is not enough evidence at the 1% level of significance to support the claim. c. reject h₀. there is enough evidence at the 1% level of significance to support the claim. d. fail to reject h₀. there is not enough evidence at the 1% level of significance to support the cla

Explanation:

To determine the correct conclusion, we analyze the logic of hypothesis testing. When we fail to reject \( H_0 \), it means we don't have enough evidence to support the alternative claim (the claim we are testing) at the given significance level (1% here). Option D states "Fail to reject \( H_0 \). There is not enough evidence at the 1% level of significance to support the claim," which aligns with the principles of hypothesis testing: if we can't reject the null, we lack sufficient evidence for the alternative (the claim). Options A is incorrect because failing to reject \( H_0 \) doesn't mean there is enough evidence for the claim. Options B and C are incorrect because rejecting \( H_0 \) would imply evidence for the claim (or against \( H_0 \)), but their reasoning about evidence availability is flawed.

Answer:

D. Fail to reject \( H_0 \). There is not enough evidence at the 1% level of significance to support the claim.