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Name: A study is conducted to compare three new appetite suppressants (A, B,
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Description: A study is conducted to compare three new appetite suppressants (A, B, and C) to a placebo in terms of their effect on weight reduction. A total of 80 participants are involved and are randomly assignned to the comparison groups in equal numbers. The

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter30: Customary And Metric Steel Rules

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Problem 8A

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A study is conducted to compare three new appetite suppressants (A, B, and C) to a placebo in terms of their effect on weight reduction. A total of 80 participants are involved and are randomly assignned to the comparison groups in equal numbers. The outcome of interest is weight reduction, measured in pounds. The data shown in the table below are observed after 3 months on treatment. Is there a significant difference in mean weight reduction among the four treatments? Use a 5% level of significance. (Hint: SST=1889)

TABLE 7-61 Weight Reduction by Treatment
A
В
C
Placebo
Mean (SD)
weight
6.4 (4.1) 8.9 (4.0) 2.2 (3.9) 2.5 (4.3)
reduction

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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