Answered: Given the following ANOVA table for…

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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Given the following ANOVA table for three treatments each with six observations:

Source	Sum of Squares	df	Mean square
Treatment	1116
Error	1068
Total	2184

a) What are the degrees of freedom for the treatment and error sources of variation?

A) 3 and 18
B) 2 and 17
C) 3 and 15
D) 2 and 15

b) What is the critical value of F at the 5% level of significance?

A) 3.29
B) 3.68
C) 3.59
D) 3.20

c) What is the treatment mean square?

A) 71.2
B) 71.4
C) 558
D) 534

d) What is the computed value of F?

A) 7.48
B) 7.84
C) 8.84
D) 8.48

e) What is the decision regarding the null hypothesis at the 5% significance level?

A) Reject H0—there is a difference in treatment means.
B) Fail to reject H0—there is a difference in treatment means.
C) Reject H0—there is a difference in errors.
D) Fail to reject H0—there is a difference in errors.

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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