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%?

Question

1537

1291

1286

1533

1223

Answer 1

Formula to find sample size:

n = [(z-value)^2 * p * q]/E^2
... where n = sample size, z-value is found using a z-table for 95% confidence (which will be 1.96), p = .30, q = 1 - p, ^2 means squared, * means to multiply, and E = .025 (2.5%)

Convert all fractions to decimals, then plug values into the formula and calculate n. Round your answer to the next highest whole number.

Answer 2

1533