Question

The Kansas Department of Revenue will take a random sample of state tax returns to estimate the proportion of taxpayers who have errors on their tax returns. What is the sample size required in order to have a maximum margin of error of 4 percentage points? (Choose the option closest to the correct value, show work.)

a. 625 b. 2500                                    c. 4 percent of the population

Answer 1

without prior estimate, let    sample proportion ,   p̂ =    0.5                          
   sampling error ,    E =   0.04                          
   Confidence Level ,   CL=   0.95                          
                                      
   alpha =   1-CL =   0.05                          
   Z value =    Zα/2 =    1.960   [excel formula =normsinv(α/2)]                      
                                      
   Sample Size,n = (Z / E)² * p̂ * (1-p̂) = (   1.960   /   0.04   ) ² *   0.50   * ( 1 -   0.50   ) =    600.2279
                                      
                                      
   so,Sample Size required=       601                          

closest option is 625

so, answer = 625