6.5 Interpreting p-Values

Part of Inference for Categorical Data: Proportions in AP® Statistics. Read the opening section, then create a free account for the full interactive lesson, practice, and progress tracking.

Start free

What Is a p-Value?

p-value

p\text{-value} = P(Z \geq z_{obs} \mid H_0 \text{ true}) \quad \text{(for right-tailed test)}

Intuition: If the null hypothesis were true, how likely is it that we'd see results at least as extreme as what we observed?

Small ${p}$ -value → the observed result is unlikely under ${H_0}$ → evidence against ${H_0}$
Large ${p}$ -value → the observed result is plausible under ${H_0}$ → no evidence against ${H_0}$

Computing p-values:

Right-tailed ( ${H_a: p > p_0}$ ): ${p = P(Z \geq z_{obs})}$
Left-tailed ( ${H_a: p < p_0}$ ): ${p = P(Z \leq z_{obs})}$
Two-tailed ( ${H_a: p \neq p_0}$ ): ${p = 2 \cdot P(Z \geq |z_{obs}|)}$

In this unit

11 lessons

Continue the full lesson in Stellar

Create a free account to unlock the remaining sections, checkpoints, course practice, and progress tracking for AP® Statistics.

Start free