Question

In an experiment to assess the effect of the angle of pull on the force required to cause separation in electrical connectors, four different angles (factor A) were used, and each of a sample of five connectors (factor B) was pulled once at each angle. The data appears in the accompanying table.

		B
		1	2	3	4	5
A	0°	45.5	42.1	39.9	36.7	45.9
	2°	44.1	44.2	38.2	38.1	47.5
	4°	42.7	42.8	42.8	42.3	48.6
	6°	43.8	45.5	47.9	37.9	56.4

Does the data suggest that true average separation force is affected by the angle of pull? State the appropriate hypotheses.

H₀: β₁ = β₂ = β₃ = β₄ = β₅ = 0
H_a: at least one β_j ≠ 0

H₀: α₁ = α₂ = α₃ = α₄ = 0
H_a: at least one α_i ≠ 0    

H₀: β₁ = β₂ = β₃ = β₄ = β₅ = 0
H_a: no β_j = 0

H₀: α₁ = α₂ = α₃ = α₄ = 0
H_a: no α_i = 0

Test the hypotheses at level 0.01 by first constructing an ANOVA table (SST = 394.89, SSA = 56.14, and SSB = 246.62). (Round your answers to two decimal places.)

Source	df	SS	MS	f	F0.01
A
B
Error
Total

State the conclusion in the problem context.

Reject H₀. The data suggests that there is an angle of pull effect.

Reject H₀. The data does not suggest that there is an angle of pull effect.    

Fail to reject H₀. The data suggests that there is an angle of pull effect.

Fail to reject H₀. The data does not suggest that there is an angle of pull effect.

Answer 1

a)

H₀: α₁ = α₂ = α₃ = α₄ = 0
H_a: at least one αi ≠ 0    

b)

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
A	56.14	3	18.71	2.44	0.12	5.95
B	246.62	4	61.66	8.03	0.00	5.41
Error	92.13	12	7.68	-	-	-
Total	394.89	19	-	-	-	-

c) Since p value for angles is 0.12, which more than 0.01. so it is not significant. therefore

Fail to reject H₀. The data does not suggest that there is an angle of pull effect.

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( extra information) However Factor B (connectors) is effective.