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° 45.1 42.2 39.6 36.8 45.8 2° 44.3 44.2 38.5 38.2 47.1 4° 42.7 42.8 42.5 42.3 48.7 6° 43.5 45.6 47.8 37.7 56.1 Does the data suggest that true average separation force is affected by the angle of pull? State the appropriate hypotheses. H0: α1 = α2 = α3 = α4 = 0 Ha: no αi = 0 H0: β1 = β2 = β3 = β4 = β5 = 0 Ha: no βj = 0 H0: α1 = α2 = α3 = α4 = 0 Ha: at least one αi ≠ 0 H0: β1 = β2 = β3 = β4 = β5 = 0 Ha: at least one βj ≠ 0 Test the hypotheses at level 0.01 by first constructing an ANOVA table (SST = 382.62, SSA = 53.39, and SSB = 239.20). (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. Fail to reject H0. The data does not suggest that there is an angle of pull effect. Reject H0. The data does not suggest that there is an angle of pull effect. Reject H0. The data suggests that there is an angle of pull effect. Fail to reject H0. The data suggests that there is an angle of pull effect.

Answer 1

Given  H0: β1 = β2 = β3 = β4 = β5 = 0 Ha: at least one βj ≠ 0

From the given data

	Antifungal Agent
Block	A	B	C	D	E	Ti	Ti^2/5
1	45.1	42.2	39.6	36.8	45.8	209.5	8778.05
2	44.3	44.2	38.5	38.2	47.1	212.3	9014.258
3	42.7	42.8	42.5	42.3	48.7	219	9592.2
4	43.5	45.6	47.8	37.7	56.1	230.7	10644.5
Tj	175.6	174.8	168.4	155	197.7	871.5	38029.01
Tj^2/4	7708.84	7638.76	7089.64	6006.25	9771.3225	38214.81

P-value of Factor B is 0.002 whcih is less than alpha 0.01 so reject H0

Thus we conclude that there is significance difference among the levels of factor B

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