A certain region would like to estimate the proportion of vo

A certain region would like to estimate the proportion of voters who intend to participate in upcoming elections. A pilot sample of 25 voters found that 17 of them intended to vote in the election. Determine the additional number of voters that need to be sampled to construct a 99% interval with a margin of error equal to 0.04 to estimate the proportion.

The region should sample (blank) additional voters

Solution

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 =    0.04  
p = 17/25 = 0.68  
      
Thus,      
      
n =    902.3459377  
      
Rounding up,      
      
n =    903 [this is the target sample size]

Thus, the additional voters needed is 903-25 = 878 [ANSWER]