A forester studies the effect of fertilization on pine fores

A forester studies the effect of fertilization on pine forests by measuring the average basal area of pine trees. In studying basal areas of similar trees for many years, he is confident these measurements are normally distributed with standard deviation 4 square inches. If he wants the sample mean to be within 1 square inch of the population mean, with probability 0.9, how many trees does he need to sample?

Solution

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.05  
      
Using a table/technology,      
      
z(alpha/2) =    1.644853627  
      
Also,      
      
s = sample standard deviation =    4  
E = margin of error =    1  
      
Thus,      
      
n =    43.28869527  
      
Rounding up,      
      
n =    44   [ANSWER]