The mean number of travel days per year for salespeople empl

The mean number of travel days per year for salespeople employed by hardware distributors needs to be estimated with a 0.50 degree of confidence. For a small pilot study the mean was 159 days and the standard deviation was 13 days. If the population mean is estimated within six days, how many salespeople should be sampled?

Solution

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.25  
      
Using a table/technology,      
      
z(alpha/2) =    0.67448975  
      
Also,      
      
s = sample standard deviation =    13  
E = margin of error =    6  
      
Thus,      
      
n =    2.135673764  
      
Rounding up,      
      
n =    3   [ANSWER]