In developing patient appointment schedules a medical center

In developing patient appointment schedules, a medical center wants to estimate the mean time that a staff member spends with each patient. How large a sample should be taken if the desired margin of error is two minutes at a 95% level of confidence? Use a planning value for the population standard deviation of eight minutes. How large a sample should be taken for a 99% level of confidence? Use a planning value for the population standard deviation of eight minutes.

Solution

a)

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 =    8  
E = margin of error =    2  
      
Thus,      
      
n =    61.46334113  
      
Rounding up,      
      
n =    62  

*****************

b)

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.005  
      
Using a table/technology,      
      
z(alpha/2) =    2.575829304  
      
Also,      
      
s = sample standard deviation =    8  
E = margin of error =    2  
      
Thus,      
      
n =    106.1583456  
      
Rounding up,      
      
n =    107   [ANSWER]