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 0.45 degree of confidence. For a small pilot study the mean was 165 days and the standard deviation was 15 days. If the population mean is estimated within eight days, how many salespeople should be sampled?

Solution

Note: I assumed that the confidence level is 95% and not 45%, becuase a 45% confidence never happens.

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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 =    15  
E = margin of error =    8  
      
Thus,      
      
n =    13.50512867  
      
Rounding up,      
      
n =    14   [ANSWER]