Question

A mail-order catalog firm designed a factorial experiment to test the effect of the size of a magazine advertisement and the advertisement design on the number of catalog requests received (data in thousands). Three advertising designs and two different size advertisements were considered. The data obtained follow Size of Advertisement Small Large Design A 8 12 12 10 B 22 26 14 28 C 10 18 24 20 Use the ANOVA procedure for factorial designs to test for any significant effects due to type of design, size of advertisement, or interaction. Use . Assume that Factor A is advertising design and Factor B is size of advertisement. Source of Variation Sum of Squares (to whole number) Degrees of Freedom Mean Square (to whole number) (to 2 decimals) -value (to 4 decimals) Factor A Factor B Interaction Error Total The value for Factor A is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 21 . What is your conclusion with respect to Factor A? - Select your answer -Factor A is significantFactor A is not significantItem 22 The value for Factor B is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 23 . What is your conclusion with respect to Factor B? - Select your answer -Factor B is significantFactor B is not significantItem 24 The value for the interaction of factors A and B is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 25 . What is your conclusion with respect to the interaction of Factors A and B? - Select your answer -The interaction of factors A and B is significantThe interaction of factors A and B is not significantItem 26 .

Answer 1

Output using excel:

Anova: Two-Factor With Replication
SUMMARY	Small	Large	Total
A
Count	2	2	4
Sum	20	22	42
Average	10	11	10.5
Variance	8	2	3.666667
B
Count	2	2	4
Sum	36	54	90
Average	18	27	22.5
Variance	32	2	38.33333
C
Count	2	2	4
Sum	34	38	72
Average	17	19	18
Variance	98	2	34.66667
Total
Count	6	6
Sum	90	114
Average	15	19
Variance	42.8	52.4
ANOVA
Source of Variation	SS	df	MS	F	P-value
Factor A	294	2	147	6.13	0.0355
Factor B	48	1	48	2.00	0.2070
Interaction	38	2	19	0.79	0.4953
Within	144	6	24
Total	524	11

For Factor A:

p-value = 0.0335

The value for Factor A is between .025 and .05 .

Conclusion with respect to Factor A:

Factor A is significant.

--------

For Factor B:

p-value = 0.2070

The value for Factor B is greater than .10

Conclusion with respect to Factor B:

Factor B is not significant.

--------

For Interaction:

p-value = 0.4953

The value for the interaction of factors A and B is greater than .10

Conclusion with respect to the interaction of Factors A and B:

The interaction of factors A and B is not significant.