Determine the sample size n needed to construct a 90 confide

Determine the sample size n needed to construct a 90% confidence interval to estimate the population proportion when p = 0.44 and the margin of error equals 5%. Click the icon to view a table of standard normal cumulative probabilities. n = (Round up to the nearest integer.)

Solution

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.05  
       
      
Using a table/technology,      
      
z(alpha/2) =    1.644853627  
      
Also,      
      
E =    0.05  
p =    0.44  
      
Thus,      
      
n =    266.6583628  
      
Rounding up,      
      
n =    267   [ANSWER]