3rd Edition

ISBN: 9781260373561

Author: Navidi, William

Publisher: MCGRAW-HILL HIGHER EDUCATION

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Chapter 9.2, Problem 66E

Statistical or practical significance: A new method of postoperative treatment was evaluated for patients undergoing a certain surgical procedure. Under the old method, the mean length of hospital stay vas 6.3 days. The sample mean for the new method was 6.1 days. A hypothesis test was performed in which the null hypothesis stated that the mean length of stay was the same for both methods, and the alternate hypothesis stated that the mean stay was lower for the new method. The P-value was 0.002. True or false:

Because the P-value is very small, we can conclude that the new method provides an important reduction in the mean length of hospital stay.
Because the P-value is very small, we can conclude that the mean length of hospital stay is less for patients treated by the new method than for patients treated by the old method.

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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Chapter 9.2, Problem 65E

Chapter 9.2, Problem 67E

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Solution Summary: The author explains that p-value is very small, which means null hypothesis can be rejected. The result is statistically significant.

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