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)TemperaturePVC1PVC2PVC3Hot (70 C)252302233276284258282277282Warm (40 C)324339303325321318302335304Cool (10 C)356377328365359336339351339

Click here for the Excel Data File

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

a.H₀:A₁A₂A₃ 0

Temperature means differH₁: All theA_jare equal to zero

Temperature means are the sameb.H₀:A₁=A₂=A₃= 0

Temperature means are the sameH₁: Not all theA_jare equal to zero

Temperature means differ

multiple choice 1

• a
• b

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

a.H₀:B₁B₂B₃ 0

PVC type means differH₁: All theB_kare equal to zero

PVC type means are the sameb.H₀:B₁=B₂=B₃= 0

PVC type means are the sameH₁: Not all theB_kare equal to zero

PVC type means differ

multiple choice 2

• a
• b

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

a.H₀: Not all theAB_jkare equal to zero

there is an interaction effectH₁: All theAB_jkare equal to zero

there is no interaction effectb.H₀: All theAB_jkare equal to zero

there is no interaction effectH₁: Not all theAB_jkare equal to zero

there is an interaction effect

multiple choice 3

• a
• b

(b)Fill in the missing data.(Round your table of means values to 1 decimal place,SSandFvalues to 2 decimal places,MSvalues to 3 decimal places, andp-values to 4 decimal places.)

Table of MeansFactor 2 (PVC Type)

Factor 1 (Temperature)PVC1PVC2PVC3TotalHot (70C)Warm (40C)Cool (10C)Total

Two-Factor ANOVA with ReplicationSourceSSdfMSFp-valueFactor 1 (Temperature)Factor 2

(PVC Type)InteractionErrorTotal

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

multiple choice 4

• 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 yourt-values andcritical values to 2 decimal places and other answers to 1 decimal place.)

Post hoc analysis for Factor 1:

Tukey simultaneous comparisont-values (d.f. = 18)

Hot (70C)Warm (40C)Cool (10C)Hot (70C)Warm (40C)Cool (10C)Critical values for experimentwise error rate:0.050.01

Post hoc analysis for Factor 2:

Tukey simultaneous comparisont-values (d.f. = 18)

PVC3PVC1PVC2PVC3PVC1PVC2Critical values for experimentwise error rate:0.050.01