Question

The data are given in the two-way table. Which variable should be used as the explanatory variable? Explain.

Study design
ANSWERED
asked 2021-08-11

A survey was designed to study how business operations vary according to their size. Companies were classified as small, medium, or large. Questionnaires were sent to 200 randomly selected businesses of each size. Because not all questionnaires were returned, researchers decided to investigate the relationship between the response rate and the size of the business. The data are given in the two-way table.
\(\text{Business size} \\ \begin{array}{l|r|r|r|r} && \text { Small } & \text { Medium } & \text { Large } & \text { Total } \\ \hline \text{Response?} & \text { Yes } & 125 & 81 & 40 & 246 \\ \hline &\text { No } & 75 & 119 & 160 & 354 \\ \hline &\text { Total } & 200 & 200 & 200 & 600 \end{array}\)
Which variable should be used as the explanatory variable? Explain.

Answers (1)

2021-08-12
A response variable (or dependent variable) is 4 variable that measures an outcomeor result ofa study, while an explanatory variable (or independent variable) is a variable that we think explains or causes changes in the response variables.
We expect the business size to influence the response as people in small businesses might be more likely to respond that people in large businesses due to having less work or more availability.
This then implies that business size is the explanatory variable.
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A survey was designed to study how business operations vary according to their size. Companies were classified as small, medium, or large. Questionnaires were sent to 200 randomly selected businesses of each size. Because not all questionnaires were returned, researchers decided to investigate the relationship between the response rate and the size of the business. The data are given in the two-way table.
\(\text{Business size} \\ \begin{array}{l|r|r|r|r} && \text { Small } & \text { Medium } & \text { Large } & \text { Total } \\ \hline \text{Response?} & \text { Yes } & 125 & 81 & 40 & 246 \\ \hline &\text { No } & 75 & 119 & 160 & 354 \\ \hline &\text { Total } & 200 & 200 & 200 & 600 \end{array}\)
Which variable should be used as the explanatory variable? Explain.

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