How large a sample is needed to estimate the true proportion of children under age 6 living in poverty in Illinois within 3% with 90% confidence?

Question

A federal report indicated that 20% of children under age 6 live in poverty in Illinois, an increase over previous years. How large a sample is needed to estimate the true proportion of children under age 6

 living in poverty in Illinois within 3% with 90% confidence? Round the intermediate calculations to three decimal places and round up your final answer to the next whole number.

n=

Answer 1

n = p * (1-p) * (z-critical value / error) ^2

p = 0.2

z-critical value = 1..645

error = 0.03

n = 0.2 * 0.8 * (1.645/0.03)^2 = 481.07.

so sample size is 482.