Question

Use the given data to find the minimum sample size required to estimate a population proportion or percentage. margin of​ error: 0.040.04​; confidence level 9595​%; modifyingabove p with caretp and modifyingabove q with caretq unknown

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