A range of values, calculated from sample data, used to estimate a population parameter.

Our best single guess for the population proportion, denoted as p̂.

A buffer zone to account for uncertainty, added and subtracted from the point estimate.

The z-score determined by the confidence level (e.g., 1.96 for 95%).

Variability of the sample proportion.

Point Estimate: Best single guess for population proportion, center of the interval | Margin of Error: Buffer zone for uncertainty, based on critical value and standard error.

Confidence Level: Success rate of the method | Confidence Interval: Range of values estimating the population parameter.

Random Sampling: Reduces bias, allows generalization to the population | Non-Random Sampling: Introduces bias, limits scope of inference.

Large Margin of Error: Less precise estimate, wider interval | Small Margin of Error: More precise estimate, narrower interval.

Using p=0.5: Finds the maximum sample size needed, conservative approach | Using Estimated p: Can result in a smaller sample size if the estimate is accurate.

$\text{Confidence Interval} = \hat{p} \pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$

n ≤ 10%N

np ≥ 10 AND n(1-p) ≥ 10

$n = \left( \frac{z^*}{ME} \right)^2 \cdot p(1-p)$

Sample proportion (p̂)