Margin of error: 0.048; confidence level: 99% ; p-hat and q-hat unknown

Question

Use the given data to find the minimum sample size required to estimate the population proportion 

Answer 1

Minimum required sample size for a desired margin of error and confidence level when it is a proportion problem:

 

n = (z²÷margin of error²)*p-hat*q-hat

The maximum value of p-hat*q-hat occurs where p-hat = .5 (found by taking the derivative of (p-hat)*(1-p-hat) and setting it equal to 0 to find the maximum.

 

n = ( 2.576²( for 99% confidence interval)÷.048² )*.5*.5 = 720.028 or 721