We guess, based on historical data, that 30% of graduating high-school seniors in a large city will have completed a first-year calculus course. What's the minimum sample size needed to construct a 95% confidence interval for a proportion with a margin of error of 2.5%?

Answer 1

Try this formula:

n = [(z-value)^2 * p * (1-p)]/E^2
...where n = sample size you need, z-value = 1.96 to represent 95% confidence, p and 1-p represent proportions, E = .025 (or 2.5%), and ^ means squared.

With your data:
n = [(1.96)^2 * .30 * .70]/.025^2

I'll let you finish the calculation. Round the answer to the next highest whole number.