A biologist wants to estimate the yield of cotton plants Bef

A biologist wants to estimate the yield of cotton plants. Before she starts the experiment, she needs to decide how many plants to grow such that the margin of error of the 95% confidence interval for the mean is 0.5. The standard deviation for the amount of cotton grown in a plant is known to be 7 ( = 7). Calculate the minimum number of plants she needs to grow to be sure her Margin of Error is less than 0.5.

Solution

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.025  
      
Using a table/technology,      
      
z(alpha/2) =    1.959963985  
      
Also,      
      
s = sample standard deviation =    7  
E = margin of error =    0.5  
      
Thus,      
      
n =    752.9259289  
      
Rounding up,      
      
n =    753   [ANSWER]