Question

​It's believed that as many as 22​% of adults over 50 never graduated from high school. We wish to see if this percentage is the same among the 25 to 30 age group.
​a) How many of this younger age group must we survey in order to estimate the proportion of​ non-grads to within 4​% with​ 90% confidence?

Answer 1

At 90% confidence interval the critical value is z_0.05 = 1.645

Margin of error = 0.04

or, z_0.05 * sqrt(p(1 - p)/n) = 0.04

or, 1.645 * sqrt(0.22 * (1 - 0.22)/n) = 0.04

or, n = (1.645 * sqrt(0.22 * 0.78)/0.04)^2

or, n = 291