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	8
	B	22	26
		14	30
	C	10	18
		18	14

Use the ANOVA procedure for factorial designs to test for any significant effects due to type of design, size of advertisement, or interaction. Use α = 0.05.

Find the value of the test statistic for type of design. (Round your answer to two decimal places.)

Find the p-value for type of design. (Round your answer to three decimal places.)

p-value =

State your conclusion about type of design.

Because the p-value ≤ α = 0.05, type of design is not significant.

Because the p-value ≤ α = 0.05, type of design is significant.    

Because the p-value > α = 0.05, type of design is significant

.Because the p-value > α = 0.05, type of design is not significant.

Find the value of the test statistic for size of advertisement. (Round your answer to two decimal places.)

Find the p-value for size of advertisement. (Round your answer to three decimal places.)

p-value =

State your conclusion about size of advertisement.

Because the p-value ≤ α = 0.05, size of advertisement is not significant.

Because the p-value ≤ α = 0.05, size of advertisement is significant.   

Because the p-value > α = 0.05, size of advertisement is significant.

Because the p-value > α = 0.05, size of advertisement is not significant.

Find the value of the test statistic for interaction between type of design and size of advertisement. (Round your answer to two decimal places.)

Find the p-value for interaction between type of design and size of advertisement. (Round your answer to three decimal places.)

p-value =

State your conclusion about interaction between type of design and size of advertisement.

Because the p-value ≤ α = 0.05, interaction between type of design and size of advertisement is not significant.

Because the p-value ≤ α = 0.05, interaction between type of design and size of advertisement is significant.    

Because the p-value > α = 0.05, interaction between type of design and size of advertisement is significant.

Because the p-value > α = 0.05, interaction between type of design and size of advertisement is not significant.

Answer 1

Solution: We can use the excel "Anova: Two-Factor With Replication" data analysis tool to find the answer to the given questions. The excel output is given below:

Anova: Two-Factor With Replication
SUMMARY	Small	Large	Total
A
Count	2	2	4
Sum	20	20	40
Average	10	10	10
Variance	8	8	5.333333
B
Count	2	2	4
Sum	36	56	92
Average	18	28	23
Variance	32	8	46.66667
C
Count	2	2	4
Sum	28	32	60
Average	14	16	15
Variance	32	8	14.66667
Total
Count	6	6
Sum	84	108
Average	14	18
Variance	27.2	72
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	344	2	172	10.75	0.010386	5.143253
Columns	48	1	48	3	0.133975	5.987378
Interaction	56	2	28	1.75	0.251932	5.143253
Within	96	6	16
Total	544	11

Use the ANOVA procedure for factorial designs to test for any significant effects due to the type of design, size of the advertisement, or interaction. Use α = 0.05.

Find the value of the test statistic for the type of design. (Round your answer to two decimal places.)

Answer:

Find the p-value for type of design. (Round your answer to three decimal places.)

State your conclusion about type of design.

Answer: Because the p-value ≤ α = 0.05, type of design is significant.    

Find the value of the test statistic for size of advertisement. (Round your answer to two decimal places.)

Answer:

Find the p-value for size of advertisement. (Round your answer to three decimal places.)

State your conclusion about size of advertisement.

Answer: Because the p-value > α = 0.05, size of advertisement is not significant.

Find the value of the test statistic for interaction between type of design and size of advertisement. (Round your answer to two decimal places.)

Answer:

Find the p-value for interaction between type of design and size of advertisement. (Round your answer to three decimal places.)

State your conclusion about interaction between type of design and size of advertisement.

Answer: Because the p-value > α = 0.05, interaction between type of design and size of advertisement is not significant.