Question

You may need to use the appropriate technology to answer this question. A mail-order catalog firm...

You may need to use the appropriate technology to answer this 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 24 24
16 28
C 8 20
16 16

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.

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

Find the value of the test statistic for size of advertisement.

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.

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 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.

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

Math   Statistics-And-Probability   
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Homework Answers

Answer #1
Two factor ANOVA
Size of Advertisement
Means:
Small Large
A 10.0 10.0 10.0
Design C 20.0 26.0 23.0
B 12.0 18.0 15.0
14.0 18.0 16.0
2 replications per cell
ANOVA table
Source SS    df MS F    p-value
Design 344.00 2 172.000 10.75 .010
Size of Advertisement 48.00 1 48.000 3.00 .134
Interaction 24.00 2 12.000 0.75 .512
Error 96.00 6 16.000
Total 512.00 11

(a) Design:

Test statistic = 10.75

p- value = 0.010

Since 0.010 < 0.05, Design is significant

(b) Size of Advertisement:

Test statistic = 3.00

p- value = 0.134

Since 0.134 > 0.05, Size of Advertisement is not significant

(c) Interaction:

Test statistic = 0.75

p- value = 0.512

Since 0.512 > 0.05, there is no significant interaction.

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