Answered: a-2) Calculate the mean and standard deviation for the difference. (Round your mean answer to 1 decimal place and standard deviation answer to 4 decimal…

MATLAB: An Introduction with Applications

6th Edition

ISBN: 9781119256830

Author: Amos Gilat

Publisher: John Wiley & Sons Inc

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Question

An experimental surgical procedure is being studied as an alternative to the old method. Both methods are considered safe. Five surgeons perform the operation on two patients matched by age, sex, and other relevant factors, with the results shown. The time to complete the surgery (in minutes) is recorded.

Surgeon 1 Surgeon 2 Surgeon 3 Surgeon 4 Surgeon 5 Old way 37 51 25 41 55 New way 29 43 21 31 59 Click here for the Excel Data File (a-1)

Calculate the difference between the new and the old ways for the data given below. Use α = .010. (Negative values should be indicated by a minus sign.) X1 X2 X1 - X2 Surgeon Old Way New Way Difference 1 37 29 8 2 51 43 8 3 25 21 4 4 41 31 10 5 55 59

(a-2) Calculate the mean and standard deviation for the difference. (Round your mean answer to 1 decimal place and standard deviation answer to 4 decimal places.)

Mean:

Standard Deviation:

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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