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 19 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 0.07 to estimate the proportion. The region should sample additional voters. (Round up to the nearest integer.)

Solution

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.005  
      
Using a table/technology,      
      
z(alpha/2) =    2.575829304  
      
Also,      
      
s = sample standard deviation =    5  
E = margin of error =    1  
      
Thus,      
      
n =    165.872415  
      
Rounding up,      
      
n =    166  

As there are already 25 voters, an additional of 166-25 = 141 is needed. [ANSWER, 141]