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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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Three samples of each of three types of PVC pipe of equal wall thickness are tested to failure under three temperature conditions, yielding the results shown below. Research questions: Is mean burst strength affected by temperature and/or by pipe type? Is there a “best” brand of PVC pipe?

Burst Strength of PVC Pipes (psi)
Temperature	PVC1	PVC2	PVC3
Hot (70º C)	247	299	239
	277	287	262
	283	275	279
Warm (40º C)	325	341	297
	322	319	315
	296	335	304
Cool (10º C)	358	375	327
	366	352	334
	338	359	340

Click here for the Excel Data File

(a-1) Choose the correct row-effect hypotheses.

a.	H₀: A₁ ≠ A₂ ≠ A₃ ≠ 0	⇐⇐ Temperature means differ
	H₁: All the A_j are equal to zero	⇐⇐ Temperature means are the same
b.	H₀: A₁ = A₂ = A₃ = 0	⇐⇐ Temperature means are the same
	H₁: Not all the A_j are equal to zero	⇐⇐ Temperature means differ

(a-2) Choose the correct column-effect hypotheses.

a.	H₀: B₁ ≠ B₂ ≠ B₃ ≠ 0	⇐⇐ PVC type means differ
	H₁: All the B_k are equal to zero	⇐⇐ PVC type means are the same
b.	H₀: B₁ = B₂ = B₃ = 0	⇐⇐ PVC type means are the same
	H₁: Not all the B_k are equal to zero	⇐⇐ PVC type means differ

(a-3) Choose the correct interaction-effect hypotheses.

a.	H₀: Not all the AB_jk are equal to zero	⇐⇐ there is an interaction effect
	H₁: All the AB_jk are equal to zero	⇐⇐ there is no interaction effect
b.	H₀: All the AB_jk are equal to zero	⇐⇐ there is no interaction effect
	H₁: Not all the AB_jk are equal to zero	⇐⇐ there is an interaction effect

(b) Fill in the missing data. (Round your table of means values to 1 decimal place, SS and F values to 2 decimal places, MS values to 3 decimal places, and p-values to 4 decimal places.)

Table of Means
	Factor 2 (PVC Type)
Factor 1 (Temperature)	PVC1	PVC2	PVC3	Total
Hot (70^º C)
Warm (40^º C)
Cool (10^º C)
Total

Two-Factor ANOVA with Replication
Source	SS	df	MS	F	p-value
Factor 1 (Temperature)
Factor 2 (PVC Type)
Interaction
Error
Total

(c) Using α = 0.05, choose the correct statement.

The main effects of temperature and PVC type are significant, but there is not a significant interaction effect.
The main effect of temperature is significant; however, there is no significant effect from PVC type or interaction between temperature and PVC type.
The main effect of PVC type is significant; however, there is no significant effect from temperature or interaction between temperature and PVC type.

(d) Perform Tukey multiple comparison tests. (Input the mean values within the input boxes of the first row and input boxes of the first column. Round your t-values and critical values to 2 decimal places and other answers to 1 decimal place.)

Post hoc analysis for Factor 1:

Tukey simultaneous comparison t-values (d.f. = 18)
	Hot (70^º C)	Warm (40^º C)	Cool (10^º C)

Hot (70^º C)
Warm (40^º C)
Cool (10^º C)
Critical values for experimentwise error rate:
	0.05
	0.01

Post hoc analysis for Factor 2:

Tukey simultaneous comparison t-values (d.f. = 18)
	PVC3	PVC1	PVC2

PVC3
PVC1
PVC2
Critical values for experimentwise error rate:
	0.05
	0.01

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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