If your p-value is $0.11$, what can you conclude at the $0.05$ significance level?

• A. There is not enough evidence to reject the null hypothesis at the $0.05$ significance level.
• B. The p-value indicates strong evidence against the null hypothesis.
• C. You should reject the null hypothesis at the $0.05$ significance level.
• D. The result is statistically significant at the $0.05$ level.

Answer: (A)

Verified step by step guidance

1. Understand that the p-value represents the probability of observing the data, or something more extreme, assuming the null hypothesis is true.
2. Recall the significance level \( \alpha \), which is the threshold for deciding whether to reject the null hypothesis. Here, \( \alpha = 0.05 \).
3. Compare the p-value to the significance level: if \( \text{p-value} < \alpha \), there is enough evidence to reject the null hypothesis; if \( \text{p-value} \geq \alpha \), there is not enough evidence to reject it.
4. Given the p-value is 0.11, which is greater than 0.05, conclude that there is not enough evidence to reject the null hypothesis at the 0.05 significance level.
5. Therefore, the result is not statistically significant at the 0.05 level, meaning we fail to reject the null hypothesis based on this p-value.