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

n ≤ 10%N

np ≥ 10 AND n(1-p) ≥ 10

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

Sample proportion (p̂)

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.

Reduces bias and allows results to be generalized to the larger population.

Ensures that one subject's data doesn't influence another's, often checked using the 10% rule.

Allows us to use the normal distribution (z-scores) for calculations; checked using the Large Counts condition.

Larger sample sizes lead to smaller standard errors, resulting in smaller margins of error and more precise estimates.

The success rate of the method, not the probability of the interval containing the true parameter.