AP Statistics / Unit 4: Inference for Quantitative Data: Means
4.2 Constructing a Confidence Interval for a Population Mean or Population Mean Difference
Notes
$$\bar x\pm t^{*}\frac{s}{\sqrt n},\quad df=n-1$$
- Conditions: random, 10%, and normal/large sample ($n\ge30$, or no strong skew or outliers in the data).
- For paired data, use the differences: $\displaystyle \bar x_d\pm t^{*}\frac{s_d}{\sqrt n}$.
Practice
Why use $t^{}$ instead of $z^{}$ for means?
Extra uncertainty from estimating $\sigma$.
$n=25$. Degrees of freedom:
$n-1$.
Before-and-after measurements on the same people should be analyzed as:
Each person gives one difference.
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