AP Statistics / Unit 3: Inference for Categorical Data: Proportions
3.13 Carrying Out a Test for the Difference Between Two Population Proportions
Notes
$$z=\frac{(\hat p_1-\hat p_2)-0}{\sqrt{\hat p_c(1-\hat p_c)\left(\frac{1}{n_1}+\frac{1}{n_2}\right)}}$$
- Find the p-value from the normal distribution; compare with $\alpha$; conclude in context.
Practice
$z=2.5$ in a one-sided test ($H_a: p_1>p_2$). The p-value is about:
Area above 2.5.
With p-value 0.006 and $\alpha=0.05$, the conclusion:
Reject $H_0$.
If the experiment used random assignment and $H_0$ is rejected, we can conclude:
Random assignment allows cause and effect.
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