AP Statistics / Unit 4: Inference for Quantitative Data: Means
4.7 Constructing a Confidence Interval for the Difference Between Two Population Means
Notes
$$(\bar x_1-\bar x_2)\pm t^{*}\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}$$
- Use technology for $df$ (or the smaller $n-1$ to be conservative).
Practice
The interval is centered at:
The point estimate.
A conservative choice of $df$:
It gives a slightly wider interval.
Two-sample $t$ procedures require:
Independence of groups.
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