Interpreting p-Values - AP Statistics

Equal to the significance level. Critical value corresponds exactly to the significance level.

Fail to reject the null hypothesis. Since $0.07 > 0.05$, insufficient evidence against $H_0$.

A p-value less than the significance level. When $p < \alpha$, results are statistically significant.

To decide whether to reject the null hypothesis. P-values provide evidence for or against $H_0$.

Null hypothesis ($H_0$). P-values are calculated assuming $H_0$ is true.

The smaller the p-value, the larger the test statistic. Larger test statistics yield smaller p-values.

$95\text{%}$. Standard confidence level when $\alpha = 0.05$.

Confidence level. Confidence level $= 1 - \alpha$.

Beta ($\beta$). The probability of incorrectly failing to reject $H_0$.

Significance level ($\text{alpha}$). The probability of incorrectly rejecting $H_0$.

$0.05$. The cutoff value for determining statistical significance.

Insufficient evidence against the null hypothesis. Large p-values suggest data is consistent with $H_0$.

Evidence against the null hypothesis. Small p-values suggest data is unlikely under $H_0$.

It determines if the null hypothesis should be rejected. Compare p-value to $\alpha$ to make rejection decision.

Type II error. Failing to reject a false null hypothesis; probability equals $\beta$.

Type I error. Rejecting a true null hypothesis; probability equals $\alpha$.

$\text{0.01}$. Used when requiring stronger evidence against $H_0$.

Fail to reject the null hypothesis. When $p > \alpha$, insufficient evidence to reject $H_0$.

Reject the null hypothesis. When $p < \alpha$, evidence against $H_0$ is strong enough.

$H_a$. Standard notation for the competing hypothesis.

$H_0$. Standard notation for the hypothesis being tested.

$\text{0.05}$. Most commonly used threshold for statistical significance.

Power increases. Higher $\alpha$ makes it easier to reject false $H_0$.

Lower p-values indicate higher statistical significance. Smaller p-values indicate stronger evidence against $H_0$.

Reject the null hypothesis. Since $0.045 < 0.05$, evidence supports rejecting $H_0$.

Both ends of the distribution for extreme values. Tests for differences in either direction from $H_0$.

The p-value decreases. Larger test statistics move further into rejection region.

Borderline decision; often interpreted as fail to reject. Exactly at threshold; convention varies by context.

Type I error. Rejecting a true null hypothesis; probability equals $\alpha$.