Question

A mail-order catalog company designed a factorial experiment to test the effect of the SIZE of a magazine advertisement and the DESIGN of the advertisement on the number of catalog requests received (measured in thousands). Three different designs were tested: A, B and C, and two different sizes were used: "Small" and "Large". The Excel-generated ANOVA output is provided below:

Source	SS	df	MS	F	PV
DESIGN	332.17	2	166.08	11.72	0.0084
SIZE	33.33	1	33.33	2.35	0.1759
Interaction	77.17	2	38.58	2.72	0.1440
Error	85	6	14.17
Total	527.67	11

If you performed the Hypothesis Test for Interaction, followed by the Hypothesis Tests for the Main Effects for Design and Size (using a 5% Significance Level), which of the following choices correctly summarizes your findings? Choose ALL correct responses.

	A.	The Size of an ad and the Design of an ad DO interact to produce a significant effect on the number of catalog requests. The SIZE of the ad does NOT have a significant effect on the number of catalog requests. The DESIGN of the ad does NOT have a significant effect on the number of catalog requests.
	B.	The Size of an ad and the Design of an ad DO interact to produce a significant effect on the number of catalog requests. The SIZE of the ad DOES have a significant effect on the number of catalog requests. The DESIGN of the ad DOES have a significant effect on the number of catalog requests.
	C.	The Size of an ad and the Design of an ad DO interact to produce a significant effect on the number of catalog requests. The SIZE of the ad DOES have a significant effect on the number of catalog requests. The DESIGN of the ad does NOT have a significant effect on the number of catalog requests.
	D.	The Size of an ad and the Design of an ad do NOT interact to produce a significant effect on the number of catalog requests. The SIZE of the ad does NOT have a significant effect on the number of catalog requests. The DESIGN of the ad DOES have a significant effect on the number of catalog requests.

Answer 1

We have to test the effect of the size & design of the magazine advertisement on the number of catalogs requests.A hypothesis test for interaction followed by the hypothesis tests for the main effects for size & design at 5% level of significance is done, so we get the anova table.we have given the p-value for design, size & interaction.

We know that if p-value is less than 0.05 (as 5% l.o.s given), we reject H0 at 5% level of significance.

Hence,

i) - For design, p-value obtained is 0.0084. Since, p-value < 0.05, we raject H0 at 5% l.os. i.e. design of an ad does have a significant effect on number of catalogs.

ii) - For size, p-value obtained is 0.1759. Since, p-value > 0.05, we accept H0 at 5% l.os. i.e. size of an ad does not have a significant effect on number of catalogs.

iii) - For interaction, p-value obtained is 0.1440. Since, p-value > 0.05, we accept H0 at 5% l.os. i.e. Size of an ad & design of an ad do not interact to produce significant effect on number of catalogs.

So, the correct option is D, i.e.

The size of an ad & design of an ad do not interact to produce significant effect on number of catalogs.

size of an ad does not have a significant effect on number of catalogs.

design of an ad does have a significant effect on number of catalogs.