AP Statistics / Unit 3: Inference for Categorical Data: Proportions
3.12 Setting Up a Test for the Difference Between Two Population Proportions
Notes
- $H_0: p_1-p_2=0$; $H_a: p_1-p_2>0$, $<0$, or $\ne0$.
- Use the pooled proportion $\displaystyle \hat p_c=\frac{x_1+x_2}{n_1+n_2}$ for conditions and standard error.
Practice
The pooled proportion with 30/100 and 50/150:
$\displaystyle \frac{80}{250}$.
Why pool in a two-proportion test?
Assume $H_0$.
The null hypothesis for a two-proportion test:
Usually no difference.
Ready for more? Take the Unit 3 test.