3 A researcher would like to estimate p the proportion of US

3. A researcher would like to estimate p, the proportion of U.S. adults who support recognizing civil unions between gay or lesbian couples. If the researcher would like to be 95% sure that the obtained sample proportion would be within 1.0% of p (the proportion in the entire population of U.S. adults), what sample size should be used?

Solution

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.025  
As there is no previous estimate for p, we set p = 0.5.      
      
Using a table/technology,      
      
z(alpha/2) =    1.959963985  
      
Also,      
      
E =    0.01  
p =    0.5  
      
Thus,      
      
n =    9603.647052  
      
Rounding up,      
      
n =    9604   [ANSWER]