AP Statistics / Unit 3: Inference for Categorical Data: Proportions
3.2 Sampling Distributions for Sample Proportions
Notes
For $\hat p$ from an SRS:
- $\mu_{\hat p}=p$, $\displaystyle \sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}$ (when $n\le10\%$ of the population).
- Approximately normal when $np\ge10$ and $n(1-p)\ge10$.
Practice
$p=0.4$, $n=100$. $\sigma_{\hat p}=$
$\displaystyle \sqrt{\frac{0.24}{100}}$.
The large counts condition for $p=0.1$ needs $n\ge$
$np\ge10$ gives $n\ge100$.
The 10% condition makes sure:
Treat draws as nearly independent.
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