A federal report indicated that 37 of children ages 2 to 5 y

A federal report indicated that 37% of children ages 2 to 5 years had a good diet an increase over previous years. How large a sample is needed to estimate the true proportion of children with good within 2% with 95% 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 =    0.37  
      
Thus,      
      
n =    2238.610128  
      
Rounding up,      
      
n =    2239   [ANSWER]