Statistics / Unit 9: Hypothesis Testing Basics
9.4 Making a Decision
Notes
Compare the p-value with the significance level $\alpha$ (commonly $0.05$).
- If p-value $\le \alpha$: reject $H_0$. The results are statistically significant and we have convincing evidence for $H_a$.
- If p-value $> \alpha$: fail to reject $H_0$. We do not have convincing evidence for $H_a$.
- Never say "accept $H_0$" or "prove $H_0$." A failure to reject does not show $H_0$ is true.
- Always state the conclusion in the context of the problem.
- Example: p-value $= 0.03$ and $\alpha = 0.05$: reject $H_0$.
Practice
A test has p-value $= 0.03$ and $\alpha = 0.05$. The decision is:
$0.03 \le 0.05$, so the result is statistically significant.
A test has p-value $= 0.12$ and $\alpha = 0.05$. The best conclusion is:
A large p-value means we fail to reject $H_0$, which is not the same as proving it.
A test has p-value $= 0.03$ and $\alpha = 0.01$. The decision is:
$0.03 > 0.01$, so the result is not significant at this level.
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