AP Statistics / Unit 3: Inference for Categorical Data: Proportions
3.3 Constructing a Confidence Interval for a Population Proportion
Notes
$$\hat p\pm z^{*}\sqrt{\frac{\hat p(1-\hat p)}{n}}$$
- Conditions: random sample, 10% condition, at least 10 successes and 10 failures.
- $z^{*}=1.96$ for 95% confidence.
Practice
$\hat p=0.6$, $n=100$. The 95% margin of error:
$\displaystyle 1.96\sqrt{\frac{0.24}{100}}\approx1.96(0.049)$.
A larger confidence level gives:
Larger $z^{*}$.
To cut the margin of error in half, multiply $n$ by:
Margin depends on $\displaystyle \frac{1}{\sqrt n}$.
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