Suppose the Total Sum of Squares (TotalSS) for a completely randomzied design with k=4 treatments and n=12 total measurements is equal to 490. In each of the following cases, conduct an F-test of the null hypothesis that the mean responses for the 4 treatments are the same. Use α=0.1. (a) The Treatment Sum of Squares (SST) is equal to 343 while the Total Sum of Squares (SST) is equal to 490. The test statistic is F= The critical value is F= The final conclusion is: A. We can reject the null hypothesis that the mean responses for the treatments are the same and accept the alternative hypothesis that at least two treatment means differ. B. There is not sufficient evidence to reject the null hypothesis that the mean responses for the treatments are the same. (b) The Treatment Sum of Squares (SST) is equal to 245 while the Total Sum of Squares (TotalSS) is equal to 490. The test statistic is F= The critical value is F= The final conclusion is: A. We can reject the null hypothesis that the mean responses for the treatments are the same and accept the alternative hypothesis that at least two treatment means differ. B. There is not sufficient evidence to reject the null hypothesis that the mean responses for the treatments are the same. (c) The Treatment Sum of Squares (SST) is equal to 441 while the Total Sum of Squares (TotalSS) is equal to 490. The test statistic is F= The critical value is F= The final conclusion is: A. There is not sufficient evidence to reject the null hypothesis that the mean responses for the treatments are the same. B. We can reject the null hypothesis that the mean responses for the treatments are the same and accept the alternative hypothesis that at least two treatment means differ.

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Description: Suppose the Total Sum of Squares (TotalSS) for a completely randomzied design with k=4 treatments and n=12 total measurements is equal to 490. In each of the following cases, conduct an F-test of the null hypothesis that the mean responses for the 4

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

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Suppose the Total Sum of Squares (TotalSS) for a completely randomzied design with k=4 treatments and n=12 total measurements is equal to 490. In each of the following cases, conduct an F-test of the null hypothesis that the mean responses for the 4 treatments are the same. Use α=0.1.

(a) The Treatment Sum of Squares (SST) is equal to 343 while the Total Sum of Squares (SST) is equal to 490.

The test statistic is F=

The critical value is F=

The final conclusion is:
A. We can reject the null hypothesis that the mean responses for the treatments are the same and accept the alternative hypothesis that at least two treatment means differ.
B. There is not sufficient evidence to reject the null hypothesis that the mean responses for the treatments are the same.

(b) The Treatment Sum of Squares (SST) is equal to 245 while the Total Sum of Squares (TotalSS) is equal to 490.

The test statistic is F=

The critical value is F=

The final conclusion is:
A. We can reject the null hypothesis that the mean responses for the treatments are the same and accept the alternative hypothesis that at least two treatment means differ.
B. There is not sufficient evidence to reject the null hypothesis that the mean responses for the treatments are the same.

(c) The Treatment Sum of Squares (SST) is equal to 441 while the Total Sum of Squares (TotalSS) is equal to 490.

The test statistic is F=

The critical value is F=

The final conclusion is:
A. There is not sufficient evidence to reject the null hypothesis that the mean responses for the treatments are the same.
B. We can reject the null hypothesis that the mean responses for the treatments are the same and accept the alternative hypothesis that at least two treatment means differ.

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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