To estimate the average time it takes to assemble a certain computer component,

Question

To estimate the average time it takes to assemble a certain computer component, the industrial engineer at an electronics firm timed 64 technicians in the performance of this task, getting a mean of 12.50 minutes and a variance of 4.00 minutes. Construct a 90 Percentage confidence interval for the true average time it takes to assemble the computer component How large a sample is needed so that the engineer will be able to assert with the confidence that the margin of error is at most 0.2 minutes

Explanation / Answer

2.

A)

Note that              
Margin of Error E = z(alpha/2) * s / sqrt(n)              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.05          
X = sample mean =    12.5          
z(alpha/2) = critical z for the confidence interval =    1.644853627          
s = sample standard deviation =    2          
n = sample size =    64          
              
Thus,              
Margin of Error E =    0.411213407          
Lower bound =    12.08878659          
Upper bound =    12.91121341          
              
Thus, the confidence interval is              
              
(   12.08878659   ,   12.91121341   ) [ANSWER]

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b)

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 =    2  
E = margin of error =    0.2  
      
Thus,      
      
n =    384.1458821  
      
Rounding up,      
      
n =    385   [ANSWER]

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