23.6 Sample Size Determination

The appropriate sample size depends on the margin of error, confidence level, and population variability. A commonly used formula for estimating the required sample size for a proportion is:

$$n = \frac{Z^2 p (1 - p)}{E^2}$$ where:

• $Z$ is the Z-score corresponding to the confidence level

• $p$ is the estimated proportion

• $E$ is the margin of error

z <- qnorm(0.975)  # 95% confidence level
p <- 0.5  # Estimated proportion
E <- 0.05  # 5% margin of error
n <- (z^2 * p * (1 - p)) / (E^2)
ceiling(n)  # Round up to nearest integer
#> [1] 385