The university data center has two main computers. The center wants to examine w
ID: 3152080 • Letter: T
Question
The university data center has two main computers. The center wants to examine whether computer 1 is receiving tasks that require processing times comparable to those of computer 2. A random sample of 13 processing times from computer 1 showed a mean of 63 seconds with a standard deviation of 15 seconds, while a random sample of 14 processing times from computer 2 (chosen independently of those for computer 1) showed a mean of 65 seconds with a standard deviation of 18 seconds. Assume that the populations of processing times are normally distributed for each of the two computers and that the variances are equal. Construct a 95% confidence interval for the difference between the mean processing time of computer 1, , and the mean processing time of computer 2, . Then complete the table below. What is the lower limit of the 95% confidence interval? What is the upper limit of the 95% confidence interval?
The university data center has two main computers. The center wants to examine whether computer 1 is receiving tasks that require processing times comparable to those of computer 2. A random sample of 13 processing times from computer 1 showed a mean of 63 seconds with a standard deviation of 15 seconds, while a random sample of 14 processing times from computer 2 (chosen independently of those for computer 1) showed a mean of 65 seconds with a standard deviation of 18 seconds. Assume that the populations of processing times are normally distributed for each of the two computers and that the variances are equal. Construct a 95% confidence interval for the difference between the mean processing time of computer 1, , and the mean processing time of computer 2, . Then complete the table below.
What is the lower limit of the 95% confidence interval?
What is the upper limit of the 95% confidence interval?
Explanation / Answer
The university data center has two main computers. The center wants to examine whether computer 1 is receiving tasks that require processing times comparable to those of computer 2. A random sample of 13 processing times from computer 1 showed a mean of 63 seconds with a standard deviation of 15 seconds, while a random sample of 14 processing times from computer 2 (chosen independently of those for computer 1) showed a mean of 65 seconds with a standard deviation of 18 seconds. Assume that the populations of processing times are normally distributed for each of the two computers and that the variances are equal. Construct a 95% confidence interval for the difference between the mean processing time of computer 1, , and the mean processing time of computer 2, . Then complete the table below. What is the lower limit of the 95% confidence interval? What is the upper limit of the 95% confidence interval?
Calculating the means of each group,
X1 = 63
X2 = 65
Calculating the standard deviations of each group,
s1 = 15
s2 = 18
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 13
n2 = sample size of group 2 = 14
Thus, df = n1 + n2 - 2 = 25
Also, sD = 6.360074642
For the 0.95 confidence level, then
alpha/2 = (1 - confidence level)/2 = 0.025
t(alpha/2) = 2.059538553
lower bound = [X1 - X2] - t(alpha/2) * sD = -15.09881892 [ANSWER]
upper bound = [X1 - X2] + t(alpha/2) * sD = 11.09881892 [ANSWER]
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