Explanation The given information is that the ANOVA data set is multiplied by a constant c . The property of mean is that it will affect change of origin and scale. Thus, the mean and total mean are affected by a factor of c. The property of standard deviation is that it will not affect change of origin, but it will affect scale. Thus, the standard deviation is affected by a factor c. Therefore, in the formulas for SSTr and SSE, replace each x i by c x i . SSTr = n 1 ( c x ¯ 1 − c x ¯ ¯ ) 2 + n 2 ( c x ¯ 2 − c x ¯ ¯ ) 2 + n 3 ( c x ¯ 3 − c x ¯ ¯ ) 2 = c 2 n 1 ( x ¯ 1 − x ¯ ¯ ) 2 + c 2 n 2 ( x ¯ 2 − x ¯ ¯ ) 2 + c 2 n 3 ( x ¯ 3 − x ¯ ¯ ) 2 = c 2 ( n 1 ( x ¯ 1 − x ¯ ¯ ) 2 + c 2 n 2 ( x ¯ 2 − x ¯ ¯ ) 2 + c 2 n 3 ( x ¯ 3 − x ¯ ¯ ) 2 ) = c 2 SSTr ( Original data ) SSE = ( n 1 − 1 ) ( c s 1 ) 2 </

Introduction to Statistics and Data Analysis

5th Edition

ISBN: 9781305445963

Author: PECK

Publisher: Cengage

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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 + ...

Chapter 15, Problem 46CR

To determine

Check the effect of MSTr, MSE, and the test statistic F.

Explain whether it is reasonable or not.

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Chapter 15 Solutions

Introduction to Statistics and Data Analysis

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Check the effect of MSTr, MSE, and the test statistic F . Explain whether it is reasonable or not.

Solution Summary: The author explains that the ANOVA data set is multiplied by a constant c. The property of mean is that it will affect change of origin and scale.

Videos

Check the effect of MSTr, MSE, and the test statistic F.

Explain whether it is reasonable or not.

Chapter 15 Solutions

Check the effect of MSTr, MSE, and the test statistic F . Explain whether it is reasonable or not.

Solution Summary: The author explains that the ANOVA data set is multiplied by a constant c. The property of mean is that it will affect change of origin and scale.

Videos

Check the effect of MSTr, MSE, and the test statistic F. Explain whether it is reasonable or not.

Chapter 15 Solutions

Check the effect of MSTr, MSE, and the test statistic F.

Explain whether it is reasonable or not.