AP Statistics / Unit 3: Inference for Categorical Data: Proportions
3.9 Sampling Distributions for the Difference Between Sample Proportions
Notes
For independent samples:
- $\mu_{\hat p_1-\hat p_2}=p_1-p_2$.
- $\displaystyle \sigma_{\hat p_1-\hat p_2}=\sqrt{\frac{p_1(1-p_1)}{n_1}+\frac{p_2(1-p_2)}{n_2}}$.
- Check large counts for both samples.
Practice
The mean of $\hat p_1-\hat p_2$:
Unbiased.
In $\sigma_{\hat p_1-\hat p_2}$, the variances:
Variances of independent variables add.
The formula requires the two samples to be:
Otherwise the variance formula fails.
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