FILLING ANOVA TABLE

Question

The partial ANOVA table below shows the results of an experiment to test the effect of two factors (A and B) on the yield in a production process. The levels of each factor were selected randomly from a larger set of levels.

(i)  (2pt).Write Ho and Ha for testing factor B.

(ii) (4pt) B was significant from the F-test. Calculate the variance component for B.

(Use the formula sheet given to help you determine the F-test, if necessary.)

ANOVA TABLE

Source	SS	d.f.	MS
A	123.0	2
B	532.1	2
Error	390.9	39
Total	1046.0	43

Answer 1

H₀: µ_B1 = µ_{B2 =} µ_B3

H_a: The means are not equal.

ANOVA TABLE

Source	SS	d.f.	MS = SS / d.f.
A	123.0	2	61.5
B	532.1	2	266.05
			Fb = MSb/MSe = 26.55
Error	390.9	39	10.02
Total	1046.0	43	p(>Fb) = 5.28 x 10-8