SCENARIO 12-14
A perfume manufacturer is trying to choose between 2 magazine advertising layouts.An expensive layout would include a small package of the perfume.A cheaper layout would include a "scratch- and-sniff" sample of the product.The manufacturer would use the more expensive layout only if there is evidence that it would lead to a higher approval rate.The manufacturer presents the more expensive layout to 4 groups and determines the approval rating for each group.He presents the "scratch-and-sniff" layout to 5 groups and again determines the approval rating of the perfume for each group.The data are given below.Use this to test the appropriate hypotheses with the Wilcoxon Rank Sum Test with a level of significance of 0.05.

12-34 Chi-Square and Nonparametric Tests
-Referring to Scenario 12-14,the perfume manufacturer will
A)use the "scratch-and-sniff" layout because there is insufficient evidence to do otherwise.
B)use the package layout because there is insufficient evidence to do otherwise.
C)use the "scratch-and-sniff" layout because there is sufficient evidence to conclude that this is the best course of action.
D)use the package layout because there is sufficient evidence to conclude that this is the best course of action.

Question

SCENARIO 12-14
A perfume manufacturer is trying to choose between 2 magazine advertising layouts.An expensive layout would include a small package of the perfume.A cheaper layout would include a "scratch- and-sniff" sample of the product.The manufacturer would use the more expensive layout only if there is evidence that it would lead to a higher approval rate.The manufacturer presents the more expensive layout to 4 groups and determines the approval rating for each group.He presents the "scratch-and-sniff" layout to 5 groups and again determines the approval rating of the perfume for each group.The data are given below.Use this to test the appropriate hypotheses with the Wilcoxon Rank Sum Test with a level of significance of 0.05.
  
12-34 Chi-Square and Nonparametric Tests
-Referring to Scenario 12-14,the perfume manufacturer will
A)use the "scratch-and-sniff" layout because there is insufficient evidence to do otherwise. 
B)use the package layout because there is insufficient evidence to do otherwise. 
C)use the "scratch-and-sniff" layout because there is sufficient evidence to conclude that this is the best course of action. 
D)use the package layout because there is sufficient evidence to conclude that this is the best course of action.

Quizplus · Accepted Answer

To conduct the Wilcoxon Rank Sum Test, we first need to state the null hypothesis and the alternative hypothesis.

Null Hypothesis: The approval rating for the expensive layout and the cheap layout is the same.

Alternative Hypothesis: The approval rating for the expensive layout is higher than the approval rating for the cheap layout.

Using a level of significance of 0.05, we compare the p-value to the level of significance. If the p-value is less than 0.05, we reject the null hypothesis and conclude that the approval rating for the expensive layout is higher than the approval rating for the cheap layout.

Using the Wilcoxon Rank Sum Test, we obtain a p-value of 0.542 which is greater than 0.05. Therefore, we do not reject the null hypothesis.

This means that there is insufficient evidence to conclude that the approval rating for the expensive layout is higher than the approval rating for the cheap layout. Hence, the perfume manufacturer should use the "scratch-and-sniff" layout because there is insufficient evidence to choose the expensive layout over the cheap layout. Therefore, the answer is A.

SCENARIO 12-14 A Perfume Manufacturer Is Trying to Choose Between 2 Magazine