gen-is-a-p-value-of-0-03-significant-at-alpha-0-05-explain-c323

Is a p-value of 0.03 significant at alpha = 0.05? Explain.

# Yes, a p-value of 0.03 is statistically significant at α = 0.05 ## The Decision Rule When conducting hypothesis testing: - **Reject the null hypothesis** if p-value ≤ α - **Fail to reject the null hypothesis** if p-value > α ## In This Case - p-value = 0.03 - α = 0.05 - Since 0.03 < 0.05, we **reject the null hypothesis** ## What This Means A p-value of 0.03 indicates there is a **3% probability** of obtaining results as extreme as (or more extreme than) what was observed, assuming the null hypothesis is true. Since this probability (3%) is less than our predetermined threshold of 5%, we conclude that the result is **statistically significant**—the evidence is strong enough to reject the null hypothesis according to our chosen significance level. ## Important Note "Statistically significant" doesn't necessarily mean "practically important" or "large effect." It simply means the result is unlikely to have occurred by chance alone, given the assumptions of the test.