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 7 13 A 11 9 23 25 Design B 15 29 10 18 с 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 a = 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 three decimal places.) p-value= State your conclusion about type of design. O Because the p-value sa = 0.05, type of design is significant. O Because the p-value > a = 0.05, type of design is significant. O Because the p-value sa = 0.05, type of design is not significant. O Because the p-value > a = 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. O Because the p-value sa = 0.05, size of advertisement is significant. O Because the p-value> a = 0.05, size of advertisement is not significant. O Because the p-value > a = 0.05, size of advertisement is significant. O Because the p-value S a = 0.05, size of advertisement is not significant.
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 7 13 A 11 9 23 25 Design B 15 29 10 18 с 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 a = 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 three decimal places.) p-value= State your conclusion about type of design. O Because the p-value sa = 0.05, type of design is significant. O Because the p-value > a = 0.05, type of design is significant. O Because the p-value sa = 0.05, type of design is not significant. O Because the p-value > a = 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. O Because the p-value sa = 0.05, size of advertisement is significant. O Because the p-value> a = 0.05, size of advertisement is not significant. O Because the p-value > a = 0.05, size of advertisement is significant. O Because the p-value S a = 0.05, size of advertisement is not significant.
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Transcribed Image Text:**Factorial Experiment Analysis on Advertisement Effectiveness**
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 recorded is displayed below:
| | Size of Advertisement |
|------------------------|-----------------------|
| | Small | Large |
| **Design** | | |
| A | 7 | 13 |
| A | 11 | 9 |
| B | 23 | 25 |
| B | 15 | 29 |
| C | 18 | 14 |
**ANOVA Procedure for Factorial Designs**
The objective is to use the ANOVA procedure for factorial designs to test for any significant effects due to type of design, size of advertisement, or their interaction. The significance level (α) is set at 0.05.
**Step-by-Step Instructions:**
1. **Calculate the Value of the Test Statistic for Type of Design:**
- Round your answer to two decimal places.
2. **Determine the p-value for Type of Design:**
- Round your answer to three decimal places.
- p-value =
3. **Conclude the Significance of Type of Design:**
- Select the appropriate conclusion based on the p-value and α (α = 0.05):
- ○ Because the p-value ≤ α = 0.05, the type of design is significant.
- ○ Because the p-value > α = 0.05, the type of design is not significant.
4. **Calculate the Value of the Test Statistic for Size of Advertisement:**
- Round your answer to two decimal places.
5. **Determine the p-value for Size of Advertisement:**
- Round your answer to three decimal places.
- p-value =
6. **Conclude the Significance of Size of Advertisement:**
- Select the appropriate conclusion based on the p-value and α:
- ○ Because the p-value ≤ α = 0.05, the size of the advertisement is significant.
- ○ Because the p-value > α = 0.05, the size of the advertisement is not significant.
7. **Calculate the Value of the Test Statistic for the Interaction Between Type
![### Interaction Between Type of Design and Size of Advertisement
**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.)*
\[ p\text{-value} = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \]
**State your conclusion about the interaction between type of design and size of advertisement.**
- \(\bigcirc\) Because the \( p \)-value \( \leq \alpha = 0.05 \), interaction between type of design and size of advertisement is significant.
- \(\bigcirc\) Because the \( p \)-value \( > \alpha = 0.05 \), interaction between type of design and size of advertisement is not significant.
- \(\bigcirc\) Because the \( p \)-value \( > \alpha = 0.05 \), interaction between type of design and size of advertisement is significant.
- \(\bigcirc\) Because the \( p \)-value \( \leq \alpha = 0.05 \), interaction between type of design and size of advertisement is not significant.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac470ff6-15fd-4fdc-a5f2-c97f7b5a1d30%2F1fa0c167-6ca7-4571-9c7e-c89c251f2573%2Ffk1cmue_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Interaction Between Type of Design and Size of Advertisement
**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.)*
\[ p\text{-value} = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \]
**State your conclusion about the interaction between type of design and size of advertisement.**
- \(\bigcirc\) Because the \( p \)-value \( \leq \alpha = 0.05 \), interaction between type of design and size of advertisement is significant.
- \(\bigcirc\) Because the \( p \)-value \( > \alpha = 0.05 \), interaction between type of design and size of advertisement is not significant.
- \(\bigcirc\) Because the \( p \)-value \( > \alpha = 0.05 \), interaction between type of design and size of advertisement is significant.
- \(\bigcirc\) Because the \( p \)-value \( \leq \alpha = 0.05 \), interaction between type of design and size of advertisement is not significant.
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