Question

We want to estimate π using a confidence interval that has a 3% margin of error, and we want to have 99% confidence that our interval captures π. We think that π is between .4 and .6. What sample size should we use?

Answer 1

Margin of error = (0.6 - 0.4)/2 = 0.1

+ E = 0.6

Or, + 0.1 = 0.6

Or, = 0.5

At 99% confidence level, the critical value is z0.005 = 2.575

Margin of error = 0.03

Or, z0.005 * sqrt((1 - )/n) = 0.03

Or, 2.575 * sqrt(0.5(1 - 0.5)/n) = 0.03

Or, n = (2.575 * sqrt(0.5 * 0.5)/0.03)^2

Or, n = 1842