Suppose that a previous study has indicated that 39 of colle

Suppose that a previous study has indicated that 39% of college math teachers are extroverts. How large of a random sample is needed to be 95% sure that a point estimate will be within a distance of 3% of p? (sample size should be a whole number)

Please make the final answer in bold so I can easily find it

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 =    0.03  
p =    0.39  
      
Thus,      
      
n =    1015.425615  
      
Rounding up,      
      
n =    1016   [ANSWER]