A real estate agent wishes to estimate to within 250 the mea

A real estate agent wishes to estimate, to within $2.50, the mean retail cost per square foot of newly built homes, with 80% confidence. He estimates the standard deviation of such costs at $5.00. Estimate the minimum size sample required.

Solution

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.1  
      
Using a table/technology,      
      
z(alpha/2) =    1.281551566  
      
Also,      
      
s = sample standard deviation =    5  
E = margin of error =    2.5  
      
Thus,      
      
n =    6.569497661  
      
Rounding up,      
      
n =    7   [ANSWER]