QUESTION 1 Use the following description for Questions 1-3. A consumer products company uses direct mail marketing for its advertising campaigns. The company has three different designs (1, 2, and 3) for a new brochure designed for customers in four regions (NE = north east, NW = north west, SE = south east, and SW = south west). The company decides to test the design types by mailing samples of each design to potential customers in each region. They repeat the direct mailing campaign 3 times for each design type and region combination and record the number of responses they receive (denoted as Response). The company wonders if the design type and region have an impact on the number of responses they get. Question 1) What type of statistical model would you use to test if the design type and region have an impact on the number of survey responses? A.) Two sample z test B.) Two sample t test C.) One-way ANOVA D.) Two-way ANOVA 2. What is/are the factors? What are its/their levels? A.) Factor is region. Region has 4 levels (NE, NW, SE, SW). B.) Factors are design and region. Design has 3 levels (Design type 1-3). Region has 4 levels (NE, NW, SE, SW). C.) Factors are design and number of survey responses. Design has 3 levels (Design type 1-3). Number of survey responses has 12 levels (Design type 1-3 for each region NE, NW, SE, SW). D.) Factors are region and number of survey responses. Region has 4 levels (NE, NW, SE, SW). Number of survey responses has 12 levels (Design type 1-3 for each region NE, NW, SE, SW). 3. Figure 1 shows the results of the statistical test without interaction term between Region and Design (aov1), and the statistical test with interaction term between Region and Design (aov2) as R output for this problem. Figure 1. (Image Uploaded) R output of model results for two statistical models, one without an interaction term between Design and Region (aov1) and one with interaction term between Design and Region (aov2). Using a significant at the significance level alpha = 0.05, based on Figure 1 which statement is correct? A.) The model without interaction (aov1) shows that the factors Design and Region are not significant with regards to their impact on survey responses at the selected significance level. B.) The model with interaction (aov2) shows that interaction term between Design and Region is significant with regards to the impact on survey responses at the selected significance level. C.) Using the model with interaction (aov2) results, we fail to reject the null hypothesis related to interaction between Design and Region at the selected significance level, i.e., we can’t reject that the levels of Design are the same with regards to the impact of Region on Response, and we can’t reject that levels of Region are the same with regards to the impact of Design on Response. D.) Using the model with interaction (aov2) results, we reject the null hypothesis related to interaction between Design and Region at the selected significance level, i.e., we reject that the levels of Design are the same with regards to the impact of Region on Response, and we reject that levels of Region are the same with regards to the impact of Design on Response.
QUESTION 1
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Use the following description for Questions 1-3.
A consumer products company uses direct mail marketing for its advertising campaigns. The company has three different designs (1, 2, and 3) for a new brochure designed for customers in four regions (NE = north east, NW = north west, SE = south east, and SW = south west). The company decides to test the design types by mailing samples of each design to potential customers in each region. They repeat the direct mailing campaign 3 times for each design type and region combination and record the number of responses they receive (denoted as Response). The company wonders if the design type and region have an impact on the number of responses they get.
Question 1)
What type of statistical model would you use to test if the design type and region have an impact on the number of survey responses?A.) Two sample z test
B.) Two sample t test
C.) One-way ANOVA
D.) Two-way ANOVA
2.
What is/are the factors? What are its/their levels?
| A.) |
Factor is region. Region has 4 levels (NE, NW, SE, SW). |
|
| B.) |
Factors are design and region. Design has 3 levels (Design type 1-3). Region has 4 levels (NE, NW, SE, SW). |
|
| C.) |
Factors are design and number of survey responses. Design has 3 levels (Design type 1-3). Number of survey responses has 12 levels (Design type 1-3 for each region NE, NW, SE, SW). |
|
| D.) |
Factors are region and number of survey responses. Region has 4 levels (NE, NW, SE, SW). Number of survey responses has 12 levels (Design type 1-3 for each region NE, NW, SE, SW). |
3.
Figure 1 shows the results of the statistical test without interaction term between Region and Design (aov1), and the statistical test with interaction term between Region and Design (aov2) as R output for this problem.
Figure 1.
(Image Uploaded)
R output of model results for two statistical models, one without an interaction term between Design and Region (aov1) and one with interaction term between Design and Region (aov2).
Using a significant at the significance level alpha = 0.05, based on Figure 1 which statement is correct?
| A.) |
The model without interaction (aov1) shows that the factors Design and Region are not significant with regards to their impact on survey responses at the selected significance level. |
|
| B.) |
The model with interaction (aov2) shows that interaction term between Design and Region is significant with regards to the impact on survey responses at the selected significance level. |
|
| C.) |
Using the model with interaction (aov2) results, we fail to reject the null hypothesis related to interaction between Design and Region at the selected significance level, i.e., we can’t reject that the levels of Design are the same with regards to the impact of Region on Response, and we can’t reject that levels of Region are the same with regards to the impact of Design on Response. |
|
| D.) |
Using the model with interaction (aov2) results, we reject the null hypothesis related to interaction between Design and Region at the selected significance level, i.e., we reject that the levels of Design are the same with regards to the impact of Region on Response, and we reject that levels of Region are the same with regards to the impact of Design on Response. |
Two way ANOVA :
The two-way analysis of variance is a statistical extension of the one-way analysis of variance that looks at the impact of two categorical independent variables on one continuous dependent variable.
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