The estimate of the population proportion is to be within pl

The estimate of the population proportion is to be within plus or minus .10, with a 99% level of confidence. The best estimate of the population proportion is .45. How large a sample is required?

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 =    0.1  
p =    0.45  
      
Thus,      
      
n =    164.2136909  
      
Rounding up,      
      
n =    165   [ANSWER]