Question

Four different coatings are being considered for corrosion protection of metal pipe. The pipe will be...

Four different coatings are being considered for corrosion protection of metal pipe. The pipe will be buried in three different types of soil. To investigate whether the amount of corrosion depends either on the coating or on the type of soil, 12 pieces of pipe are selected. Each piece is coated with one of the four coatings and buried in one of the three types of soil for a fixed time, after which the amount of corrosion (depth of maximum pits, in 0.0001 in.) is determined. The data appears in the table.

Soil Type (B)
  1     2     3  
Coating (A)   1   62 47 51
2 53 51 45
3 48 45 50
4 50 41 50

(a) Assuming the validity of the additive model, carry out the ANOVA analysis using an ANOVA table to see whether the amount of corrosion depends on either the type of coating used or the type of soil.
State the appropriate hypotheses for the coating effect.

H0A: α1α2α3α4
HaA: at least one αi = 0H0A: α1α2α3α4
HaA: all αi's = 0    H0A: α1 = α2 = α3 = α4 = 0
HaA: at least one αi ≠ 0H0A: α1 = α2 = α3 = α4 = 0
HaA: no αi = 0


State the appropriate hypotheses for the soil type factor.

H0B: β1β2β3
HaB: at least one βj = 0H0B: β1 = β2 = β3 = 0
HaB: at least one βj ≠ 0    H0B: β1 = β2 = β3 = 0
HaB: no βj = 0H0B: β1β2β3
HaB: all βj's are equal


Complete the ANOVA table. Use α = 0.05. (Round your answers to two decimal places.)

Source df SS MS f F0.05
A                         
B
Error
Total


What can you conclude for H0A?

Fail to reject H0A. The data suggests that there is a coating effect.Reject H0A. The data suggests that there is a coating effect.    Fail to reject H0A. The data does not suggest that there is a coating effect.Reject H0A. The data does not suggest that there is a coating effect.


What can you conclude for H0B?

Reject H0B. The data suggests that there is a soil type effect.Reject H0B. The data does not suggest that there is a soil type effect.    Fail to reject H0B. The data suggests that there is a soil type effect.Fail to reject H0B. The data does not suggest that there is a soil type effect.


(b) Compute the model parameters. (Round your answers to two decimal places.)

=
1 =
2 =
3 =
4 =
1 =
2 =
3 =

Homework Answers

Answer #1

a)

H0A: α1 = α2 = α3 = α4 = 0
HaA: at least one αi ≠ 0

H0B: β1 = β2 = β3 = 0
HaB: at least one βj ≠ 0

Applying two way ANOVA: (use excel: data: data analysis: two way ANOVA: without replication select Array):
Source of Variation df SS MS F F crit
A 3 72.92 24.31 1.26 4.76
B 2 106.17 53.08 2.75 5.14
Error 6 115.83 19.31
Total 11 294.92

  Fail to reject H0A. The data does not suggest that there is a coating effect.

Fail to reject H0B. The data does not suggest that there is a soil type effect.

b)

µ = 49.42
α1 = 3.92
α2 = 0.25
α3 = -1.75
α4 = -2.42
ß1 = 3.83
ß2 = -3.42
ß3 = -0.42
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