Corn: In a prior sample of corn, farmer Carl finds that 16% of the sample has wo

Question

Corn: In a prior sample of corn, farmer Carl finds that 16% of the sample has worms but the margin of error for his population estimate was too large. He wants an estimate that is in error by no more than 2.5 percentage points at the 95% confidence level. Enter your answers as whole numbers. (a) What is the minimum sample size required to obtain this type of accuracy? Use his prior sample proportion in your calculation. (b) What is the minimum sample size required to obtain this type of accuracy when you assume no prior knowledge of the sample proportion?

Explanation / Answer

a)

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 =    0.025  
p =    0.16  
      
Thus,      
      
n =    826.0673048  
      
Rounding up,      
      
n =    827   [ANSWER]

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b)

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 =    0.025  
p =    0.5  
      
Thus,      
      
n =    1536.583528  
      
Rounding up,      
      
n =    1537   [ANSWER]

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