The third shift at the Microsoft\'s Windows security unit in Redmond, Washington

Question

The third shift at the Microsoft's Windows security unit in Redmond, Washington is considering replacing its coffee brewing units with new German-made brewers. As the newest member of this elite Microsoft team, you have been assigned to investigate this proposal. Develop a 99 percent confidence interval for the average yield (cups per pound) for the new German coffee brewer. The margin of error should be no bigger than 0.3 (three tenths of a cup). Based on experience with the current coffee makers, your best guess for the population standard deviation, sigma, is 1.2 cups. How big of a sample do you need? Calculate the estimated sample size needed for the above scenario and communicate your findings to the business manager.

Explanation / Answer

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 =    1.2  
E = margin of error =    0.3  
      
Thus,      
      
n =    106.1583456  
      
Rounding up,      
      
n =    107   [ANSWER]

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