Suppose you conduct a hypothesis test and your p-value is equal to $0.13$. What can you conclude at a significance level of $0.05$?

• A. Fail to reject the null hypothesis because $0.13$ is greater than $0.05$.
• B. There is strong evidence against the null hypothesis.
• C. Reject the null hypothesis because $0.13$ is less than $0.05$.
• D. The result is statistically significant at the $0.05$ level.

Answer: (A)

Verified step by step guidance

1. Identify the null hypothesis (H0) and the alternative hypothesis (H1) for the test you conducted.
2. Note the given p-value, which is 0.13, and the significance level \( \alpha = 0.05 \).
3. Compare the p-value to the significance level: if \( p \leq \alpha \), reject the null hypothesis; if \( p > \alpha \), fail to reject the null hypothesis.
4. Since \( 0.13 > 0.05 \), you fail to reject the null hypothesis, meaning there is not enough evidence to support the alternative hypothesis.
5. Conclude that the result is not statistically significant at the 0.05 level, so you do not have strong evidence against the null hypothesis.