AP®︎ Statistics: Topic 3.6 Flashcards

Probability, assuming H₀ is true, of getting a test statistic as extreme or more extreme than the observed one, in the direction specified by Hₐ; not the probability that H₀ is true

The probability distribution of possible test-statistic values from repeated samples if H₀ were true

For Hₐ: p > p₀, the p-value is P(Z ≥ z_obs), or in simulation, the proportion of statistics at or above z_obs

For Hₐ: p < p₀, the p-value is P(Z ≤ z_obs), or in simulation, the proportion of statistics at or below z_obs

For Hₐ: p ≠ p₀, the p-value is P(Z ≤ -|z_obs|) + P(Z ≥ |z_obs|), equivalently 2P(Z ≥ |z_obs|)); in simulation, the proportion at or below -|z_obs| plus the proportion at or above |z_obs|.

The proportion of simulated test statistics in the null distribution that are as extreme or more extreme than the observed statistic, in the direction of Hₐ.

The observed result would be unusual if H₀ were true, so it is evidence against H₀ and in favor of Hₐ; smaller p-values mean stronger evidence

The observed result would not be unusual if H₀ were true, so it does not provide convincing evidence for Hₐ; it does not show that H₀ is true

Defined by Hₐ: outcomes in the direction of the alternative at least as far from the null result as the observed statistic; for two-sided tests, in either direction using |z_obs|.