Question

The following observations were obtained when conducting a two-way ANOVA experiment with no interaction

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					Factor A
Factor B				1				2				3				4				X⎯⎯⎯jX¯j for Factor B
	1				5				2				2				1				2.500
	2				9				6				9				8				8.000
	3				15				11				13				16				13.750
X−iX−i for Factor A				9.667					6.000				8.000			8.333				X⎯⎯⎯⎯⎯⎯=8.083X¯¯⁢ = 8.083

a. Calculate SST, SSA, SSB, and SSE. (Round intermediate calculations to at least 4 decimal places. Round your answers to 2 decimal places.)

b. Calculate MSA, MSB, and MSE. (Round intermediate calculations to at least 4 decimal places. Round your answers to 2 decimal places.)

c. Construct an ANOVA table. (Round intermediate calculations to at least 4 decimal places. Round "SS", "MS" to 2 decimal places, "F" 3 decimal places.)

d. At the 10% significance level, do the levels of Factor B differ?

• Yes, since we reject the null hypothesis.

• No , since we reject the null hypothesis.

• Yes, since we do not reject the null hypothesis.

• No, since we do not reject the null hypothesis.

e. At the 10% significance level, do the levels of Factor A differ?

• Yes, since we reject the null hypothesis.

• No, since we reject the null hypothesis.

• Yes, since we do not reject the null hypothesis.

• No, since we do not reject the null hypothesis.

Answer 1

Applying ANOVA"

Source of Variation	SS	df	MS	F	P-value
factor B	253.1667	2	126.5833	59.1818	0.0001
factor A	16.9167	3	5.6389	2.6364	0.1442
Error	12.8333	6	2.1389
Total	282.9167	11

a)

SST=282.92

, SSA=16.92

SSB=253.17,

and SSE=12.83

b)

MSA=5.64

, MSB,=126.58

and MSE=2.14

c)

Source of Variation	SS	df	MS	F	P-value
factor B	253.17	2	126.58	59.182	0.0001
factor A	16.92	3	5.64	2.636	0.1442
Error	12.83	6	2.14
Total	282.92	11

d) Yes, since we reject the null hypothesis.

e)

No, since we do not reject the null hypothesis.