AP Statistics / Unit 4: Inference for Quantitative Data: Means
4.1 Sampling Distributions for Sample Means
Notes
For $\bar x$ from an SRS of size $n$:
- $\mu_{\bar x}=\mu$; $\displaystyle \sigma_{\bar x}=\frac{\sigma}{\sqrt n}$ (10% condition).
- Normal if the population is normal, or approximately normal if $n\ge30$ (CLT).
Practice
$\sigma=12$, $n=36$. $\sigma_{\bar x}=$
$\displaystyle \frac{12}{6}$.
A population is skewed and $n=10$. Is $\bar x$'s distribution approximately normal?
The CLT needs a large $n$.
The center of the sampling distribution of $\bar x$:
$\bar x$ is unbiased.
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