If you perform a test with p-value 0.051 and alpha 0.05, what is the correct conclusion?

If you perform a test with p-value 0.051 and alpha 0.05, what is the correct conclusion?

• A. Do not reject the null at 5% significance.
• B. Reject the null.
• C. The result is inconclusive.
• D. The alternative is proven.

Answer: (A)

The key idea is how p-value and significance level relate to the decision about the null hypothesis. The p-value tells you how compatible the observed data are with the null assumption; the significance level (alpha) sets the threshold for how strong that evidence must be to declare a result statistically significant. The rule is to reject the null only if the p-value is less than or equal to alpha. Here, the p-value is 0.051 and the significance level is 0.05. Since 0.051 is just above 0.05, there isn’t enough evidence at the 5% level to conclude that the alternative hypothesis holds. So you do not reject the null at 5% significance. This doesn’t prove the null is true; it simply means the observed effect isn’t statistically significant under this threshold. If you used a higher alpha, you might reach a rejection; with a lower alpha, you’d be even less likely to reject.

The key idea is how p-value and significance level relate to the decision about the null hypothesis. The p-value tells you how compatible the observed data are with the null assumption; the significance level (alpha) sets the threshold for how strong that evidence must be to declare a result statistically significant. The rule is to reject the null only if the p-value is less than or equal to alpha.

Here, the p-value is 0.051 and the significance level is 0.05. Since 0.051 is just above 0.05, there isn’t enough evidence at the 5% level to conclude that the alternative hypothesis holds. So you do not reject the null at 5% significance. This doesn’t prove the null is true; it simply means the observed effect isn’t statistically significant under this threshold. If you used a higher alpha, you might reach a rejection; with a lower alpha, you’d be even less likely to reject.