AP Statistics / Unit 4: Inference for Quantitative Data: Means
4.6 Sampling Distributions for the Difference Between Two Sample Means
Notes
For independent samples:
- $\mu_{\bar x_1-\bar x_2}=\mu_1-\mu_2$.
- $\displaystyle \sigma_{\bar x_1-\bar x_2}=\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}$.
Practice
$\sigma_1=6$, $n_1=9$, $\sigma_2=8$, $n_2=16$. $\sigma_{\bar x_1-\bar x_2}=$
$\displaystyle \sqrt{4+4}$.
The mean of $\bar x_1-\bar x_2$:
Unbiased.
The shape is approximately normal when:
Both need normal or large samples.
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