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 0.85 degree of confidence. For a small pilot study the mean was 160 days and the standard deviation was 22 days. If the population mean is estimated within five days, how many salespeople should be sampled?

a. 2455

b. 41

c. 761

d. 618

Solution

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.075  
      
Using a table/technology,      
      
z(alpha/2) =    1.439531471  
      
Also,      
      
s = sample standard deviation =    22  
E = margin of error =    5  
      
Thus,      
      
n =    40.11877657  
      
Rounding up,      
      
n =    41   [ANSWER]