Answered: The Engineering group performed a…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section11.2: Box-and-whisker Plots

Problem 1E

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Question

The Engineering group performed a factorial experiment to investigate the effect of paint primer type and application method on paint adhesion. The results for each combination of primer type and application method are shown below. Each combination has three specimens painted, then a finish paint was applied, and the adhesion force was measured. Compute for the following: (1) Sum of Squares, Degrees of Freedom, (3) Mean Square, (4) fo, and (5) P-Value for; (a) Primer types, (b) Application methods, (c) Interaction, (d) Error, and (e) Total. Write your complete solution and create a table for the results

ANSWER 1,2,3,4

Primer Type
1
2
3
yi
Adhesion Force Data
Dipping
Sum
Spraying
4.2 4.7 4.2 ? 5.6 5.1 5.8
5.7 5.2 5.0
?
4.0 3.9 3.9
?
?
Sum yi
?
?
6.1 5.9 6.4 ?
5.2 5.3 5.2
?
?
....
?
?
?

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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