To calculate the minimum sample size needed for a 95% confidence interval with a margin of error of 2.5%, we can use the formula:
n = (Z^2 * p * (1-p)) / E^2
Where:
n = sample size
Z = z-score for a 95% confidence interval (1.96)
p = estimated proportion (0.30)
E = margin of error (0.025)
Plugging in the values:
n = (1.96^2 * 0.30 * (1-0.30)) / 0.025^2
n = (3.8416 * 0.30 * 0.70) / 0.000625
n = (0.808608) / 0.000625
n = 1293.7728
Since we can't have a fraction of a person in a sample, we need to round up to the nearest whole number. Therefore, the minimum sample size needed is 1,294, which is closest to option B.
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%?
A. 323
B. 1, 291
C. 1, 290
D. 1,536
Ε. 1,537
1 answer