16 Enough eggs One of the important issues for poultry farm

16. Enough eggs? - One of the important issues for poultry farmers is the production rate - the percentage of days on which a given hen actually lays an egg. Ideally, that would be 100% (an egg every day), but realistically, hens tend to lay eggs on about 3 of every 4 days. ISA Babcock wants to advertise the production rate for the B300 Later (see Exercise 14) as a 95% confidence interval with a margin of error of + or - 2%. How many hens must they collect data on?

Solution

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.025  
As there is no previous estimate for p, we set p = 0.5.      
      
Using a table/technology,      
      
z(alpha/2) =    1.959963985  
      
Also,      
      
E =    0.02  
p =    0.5  
      
Thus,      
      
n =    2400.911763  
      
Rounding up,      
      
n =    2401   [ANSWER]