The president of a university wants to estimate the proporti

The president of a university wants to estimate the proportion of students who will graduate from the arts school and will then start an MBA program. She want the estimate to be within 2% of the true percentage. Data from the past indicated a sample percentage of 19%. How much larger must this sample be? Use a 95% level of confidence.

Solution

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.025  
       
      
Using a table/technology,      
      
z(alpha/2) =    1.959963985  
      
Also,      
      
E =    0.02  
p =    0.19  
      
Thus,      
      
n =    1478.001281  
      
Rounding up,      
      
n =    1479   [ANSWER, TARGET SAMPLE SIZE]