Many states are carefully considering steps that would help

Many states are carefully considering steps that would help them collect sales taxes on items purchased through the Internet. How many randomly selected sales transactions must be surveyed to determine the percentage that transpired over the Internet? Assume that we want to be 99% confident that the sample percentage is within five percentage points of the true population percentage for all sales transactions.

n= ???

Solution

As we don\'t have a previous estimate of p, then we assume p = 0.50, the worst case scenario.

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.005  
      
Using a table/technology,      
      
z(alpha/2) =    2.575829304  
      
Also,      
      
E =    0.05  
p =    0.5  
      
Thus,      
      
n =    663.4896601  
      
Rounding up,      
      
n =    664 [ANSWER]