Math Problem Statement

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Topic 6 Homework (Nonadaptive) Question 3 of 11 (1 point)|Question Attempt: 1 of Unlimited

1 2 3 4 5 6 7 8 9 10 11 Question 3 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 10 processing times from computer 1 showed a mean of 59 seconds with a standard deviation of 16 seconds, while a random sample of 13 processing times from computer 2 (chosen independently of those for computer 1) showed a mean of 70 seconds with a standard deviation of 20 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 −μ1μ2 between the mean processing time of computer 1, μ1, and the mean processing time of computer 2, μ2. Then find the lower limit and upper limit of the 95% confidence interval. Carry your intermediate computations to at least three decimal places. Round your responses to at least two decimal places. (If necessary, consult a list of formulas.)

Lower limit: Upper limit:

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Math Problem Analysis

Mathematical Concepts

Statistics
Confidence Intervals
t-Distribution

Formulas

Pooled standard deviation formula: sp = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2))
Standard error formula: SE = sp * sqrt(1/n1 + 1/n2)
Confidence interval formula: (x̄1 - x̄2) ± t * SE

Theorems

Central Limit Theorem
t-Distribution Theorem

Suitable Grade Level

College/University