Instruction 19-3
A perfume manufacturer is trying to choose between two 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 both layouts to five groups and determines the approval rating from each group on both layouts. The data are given below. Use this to test whether the median difference in approval rating is different from zero in favour of the more expensive layout with a level of significance of 0.05.
$\begin{array}{cc}
\text { Padkage } & \text { Scratch } \
\hline 52 & 37 \
68 & 43 \
43 & 53 \
48 & 39 \
56 & 47
\end{array}$

-Referring to Instruction 19-3,the perfume manufacturer will ____.
A) use the package layout because there is sufficient evidence to conclude that this is the best course of action
B) use the "scratch-and-sniff" 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 insufficient evidence to do otherwise

Question

Instruction 19-3
A perfume manufacturer is trying to choose between two 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 both layouts to five groups and determines the approval rating from each group on both layouts. The data are given below. Use this to test whether the median difference in approval rating is different from zero in favour of the more expensive layout with a level of significance of 0.05.
 $\begin{array}{cc}
\text { Padkage } & \text { Scratch } \
\hline 52 & 37 \
68 & 43 \
43 & 53 \
48 & 39 \
56 & 47
\end{array}$

-Referring to Instruction 19-3,the perfume manufacturer will ____.
A) use the package layout because there is sufficient evidence to conclude that this is the best course of action
B) use the "scratch-and-sniff" 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 insufficient evidence to do otherwise

Quizplus · Accepted Answer

We need to test if there is a significant difference in approval rating between the more expensive package layout and the cheaper scratch-and-sniff layout. We can use a non-parametric test, such as the Wilcoxon signed-rank test, to compare the medians of the paired data. The null hypothesis is that there is no difference in median approval rating between the two layouts. Using a significance level of 0.05, we find that the test statistic is not significant (p>0.05), indicating that we fail to reject the null hypothesis. This means there is insufficient evidence to conclude that the more expensive layout leads to a higher approval rate. Therefore, the perfume manufacturer should use the cheaper scratch-and-sniff layout.

Instruction 19-3 a Perfume Manufacturer Is Trying to Choose Between Padkage Scratch 52376843435348395647\begin{array}{cc}\text { Padkage } & \text { Scratch } \\\hline 52 & 37 \\68 & 43 \\43 & 53 \\48 & 39 \\56 & 47\end{array} Padkage 5268434856​ Scratch 3743533947​​

Instruction 19-3
a Perfume Manufacturer Is Trying to Choose Between $\begin{array}{cc}\text { Padkage } & \text { Scratch } \\\hline 52 & 37 \\68 & 43 \\43 & 53 \\48 & 39 \\56 & 47\end{array}$