Question

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 63 47 51 54 51 47 49 45 50 51 41 51 What can you conclude for HOA? Reject Hon. The data suggests that there is a coating effect. Fail to reject Hox. The data suggests that there is a coating effect. Fail to reject Ho. The data does not suggest that there is a coating effect. Reject Hon. The data does not suggest that there is a coating effect. Coating (A) What can you conclude for HOB? Reject Hon. The data does not suggest that there is a soil type effect. Fail to reject Hos: The data does not suggest that there is a soil type effect. Fail to reject Hog. The data suggests that there is a soil type effect. Reject Hop. The data suggests that there is a soil type effect. (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. O H a , ***a, ** Han: at least one a = 0 O Hora* ,#az #a Han: all a's = 0 O Hor: a = a 2 = = a, = 0 Han: at least one a; = 0 (b) Compute the model parameters. (Round your answers to two decimal places.) << - Hai a = x2 = a + a = 0 Haa: no « = 0 State the appropriate hypotheses for the soil type factor. O HOB: 8, 7B, * B3 Habi all 8's are equal O HOB: 8, 7B, * B3 Hagi at least one B, = 0 O HOB: 8. = B= B3 = 0 Hagi at least one B, = 0 Hog: 8. = B2 = 0 Hagi no B, = 0 Complete the ANOVA table. Use a = 0.05. (Round your answers to two decimal places.) Source df SS MS f F0.05 Error Total

Answer 1

O Hor: a = < = az = x, = 0 Han: at least one a = 0

Hos: B. = B2 = 8z = 0 Habi at least one B, = 0

Applying two way ANOVA: (use excel: data: data analysis: two way ANOVA: without replication select Array):

Source of Variation	df	SS	MS	F		F0..05
A	3	70	23.33	1.30		4.76
B	2	136.5	68.25	3.81		5.14
Error	6	107.5	17.92
Total	11	314

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

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

b)

μ =50

α̂1 =	3.67
α̂2 =	0.67
α̂2 =	-2.00
α̂2 =	-2.33

β̂1 =	4.25
β̂2 =	-4.00
β̂2 =	-0.25