A local health center noted that in a sample of 400 patients

A local health center noted that in a sample of 400 patients 80 were referred to them by the local hospital. What size sample would be required to estimate the proportion of hospital referrals with a margin of error of 0.08 or less at 95% confidence?

Select one:

A. 80

B. 89

C. 91

D. 97

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 =    0.08  
p = 80/400 =   0.2  
      
Thus,      
      
n =    96.03647052  
      
Rounding up,      
      
n =    97   [ANSWER]