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A small computer network consists of ten users and one printer. The average turn

ID: 3380400 • Letter: A

Question

A small computer network consists of ten users and one printer. The average turn around time for the system is 15 minutes. Ten new users and a second printer are added to the system. A sample of 30 turnaround times for the new network yields an average turnaround time of X = 14 and a sample variance of s^2 = 0. Calculate the 95% confidence interval for the mean turnaround time. Is there evidence to support the assertion that the modifications to the system have had no effect on turnaround times?

Explanation / Answer

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 =    0.025          
X = sample mean =    14          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    3          
n = sample size =    30          
              
Thus,              
Margin of Error E =    1.073516486          
Lower bound =    12.92648351          
Upper bound =    15.07351649          
              
Thus, the confidence interval is              
              
(   12.92648351   ,   15.07351649   ) [ANSWER]

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b)

Yes, there is evidence, as the old turnaround time, 15 minutes, is still inside the confidence inetrval.