a newspaper article about the results of a poll states in th

a newspaper article about the results of a poll states: \"in theory, the results of such a poll, in 99 cases out of 100 should differ by no more than 3 percentage points in either direction from what would have been optained by interviewing all voters in the united states. \" Find the sample size suggested by this statement

Solution

It suggests a 99% confidence, and margin of error of 0.03.

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.005  
As there is no previous estimate for p, we set p = 0.5.      
      
Using a table/technology,      
      
z(alpha/2) =    2.575829304  
      
Also,      
      
E =    0.03  
p =    0.5  
      
Thus,      
      
n =    1843.026834  
      
Rounding up,      
      
n =    1844   [ANSWER]