If a p-value is 0.03, what does this imply at a 5% significance level?

• A. The null hypothesis is true.
• B. The result is statistically significant at the 5% level.
• C. The alternative hypothesis is proven.
• D. There is a 3% probability that the null is true.

Answer: (B)

Interpreting p-values in hypothesis testing means understanding what the observed data say under the assumption that the null hypothesis is true. A p-value of 0.03 is the probability of obtaining results as extreme as what was observed (or more) if the null is in fact true.

At a 5% significance level, you compare this p-value to 0.05. Since 0.03 is less than 0.05, you reject the null at the 5% level. This indicates the result is statistically significant at that level, providing evidence against the null hypothesis.

It’s important to note that this does not prove the alternative hypothesis or give the probability that the null is true. It simply shows that the observed data would be quite unlikely under the null, enough to meet the 5% criterion.