Answered: Design and Analysis of Experiment using…

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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Question

Design and Analysis of Experiment using the statistical technique one-way Anova.

Use Minitab software to solve the problem.

Problem: A chemical engineer wants to compare the hardness of four blends of paint. Six samples of each paint blend were applied to a piece of metal. The pieces of metal were cured. Then each sample was measured for hardness. Test for the equality of means and assess the differences between pairs of means using one-way Anova and Fisher's LSD multiple comparison of means. Interpret the results and draw conclusions.

For the data of the problem, see the picture.

Give some data analysis, conclusion, and some reflections too.

C1-T
C2
C3
C4
Paint
Hardness Temp Operator
1
Blend 2
14.9
30.3
1
Blend 3
13.0
30.9
Blend 4
15.0
30.5
2
4
Blend 1
17.0
29.4
3
Blend 1
13.9
30.0
3
Blend 3
16.4
29.6
1
7
Blend 1
10.4
29.6
2
8
Blend 2
3.2
29.9
2
Blend 2
1.9
28.9
10
Blend 2
7.3
28.6
1
11
Blend 4
17.8
30.8
3
12
Blend 2
9.6
30.8
13 Blend 4
22.9
28.9
1
14 Blend 4
17.4
30.6
15 Blend 3
13.3
29.8
16
Blend 1
19.3
30.0
1
17
Blend 1
16.1
29.9
18
Blend 3
6.5
30.6
2
19
Blend 1
11.7
30.1
20
Blend 4
16.9
30.7
3
21 Blend 4
18.4
29.9
1
22 Blend 3
11.9
29.5
23
Blend 2
14.5
29.9
1
24
Blend 3
16.8
29.9
2.

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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