In a completely randomized experimental design, 7 experimental units were used for the first treatment, 9 experimental units for the second treatment, and 14 experimental units for the third treatment. Part of the ANOVA table for this experiment is shown below. Source of Sum of Degrees of Mean Variation Squares Freedom Square F BetweenTreatments ---------? ----------- ? ----------? 4.5 Error (Within Treatments) ---------? ------------? 4 Total ---------? -----------? Fill in all the blanks in the above ANOVA table. State the null and alternative hypotheses to test whether there is a significant difference among the means. Using the p- value approach, what is your conclusion? Let Level of significance=.05

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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In a completely randomized experimental design, 7 experimental units were used for the first treatment, 9 experimental units for the second treatment, and 14 experimental units for the third treatment. Part of the ANOVA table for this experiment is shown below.

Source of Sum of Degrees of Mean Variation Squares Freedom Square F

BetweenTreatments ---------? ----------- ? ----------?

4.5

Error (Within Treatments) ---------? ------------? 4

Total ---------? -----------?

Fill in all the blanks in the above ANOVA table.
State the null and alternative hypotheses to test whether there is a significant difference among the means.
Using the p- value approach, what is your conclusion? Let Level of significance=.05

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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