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 Aj are equal to zero ⇐⇐ Temperature means are the same b. H0: A1 = A2 = A3 = 0 ⇐⇐ Temperature means are the same H1: Not all the Aj are equal to zero ⇐⇐ Temperature means differ a b (a-2) Choose the correct column-effect hypotheses. a. H0: B1 ≠ B2 ≠ B3 ≠ 0 ⇐⇐ PVC type means differ H1: All the Bk 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 Bk are equal to zero ⇐⇐ PVC type means differ a b (a-3) Choose the correct interaction-effect hypotheses. a. H0: Not all the ABjk are equal to zero ⇐⇐ there is an interaction effect H1: All the ABjk are equal to zero ⇐⇐ there is no interaction effect b. H0: All the ABjk are equal to zero ⇐⇐ there is no interaction effect H1: Not all the ABjk are equal to zero ⇐⇐ there is an interaction effect a b (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 (70º C) Warm (40º C) Cool (10º 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 (70º C) Warm (40º C) Cool (10º C) Hot (70º C) Warm (40º C) Cool (10º 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

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 Aj are equal to zero ⇐⇐ Temperature means are the same b. H0: A1 = A2 = A3 = 0 ⇐⇐ Temperature means are the same H1: Not all the Aj are equal to zero ⇐⇐ Temperature means differ a b (a-2) Choose the correct column-effect hypotheses. a. H0: B1 ≠ B2 ≠ B3 ≠ 0 ⇐⇐ PVC type means differ H1: All the Bk 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 Bk are equal to zero ⇐⇐ PVC type means differ a b (a-3) Choose the correct interaction-effect hypotheses. a. H0: Not all the ABjk are equal to zero ⇐⇐ there is an interaction effect H1: All the ABjk are equal to zero ⇐⇐ there is no interaction effect b. H0: All the ABjk are equal to zero ⇐⇐ there is no interaction effect H1: Not all the ABjk are equal to zero ⇐⇐ there is an interaction effect a b (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 (70º C) Warm (40º C) Cool (10º 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 (70º C) Warm (40º C) Cool (10º C) Hot (70º C) Warm (40º C) Cool (10º 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

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Description: 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 typ

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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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

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