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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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. H0A1 ≠ A2 ≠ A3 ≠ 0 ⇐⇐ Temperature means differ
  H1: All the Aj are equal to zero ⇐⇐ Temperature means are the same
b. H0A1 = 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. H0B1 ≠ B2 ≠ B3 ≠ 0 ⇐⇐ PVC type means differ
  H1: All the Bk are equal to zero ⇐⇐ PVC type means are the same
b. H0B1 = 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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