When performing a hypothesis test upon dependent samples, the variable interest is...

I think it is the differences that exist between the matched-pairs data.

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You are correct! When performing a hypothesis test on dependent samples, the variable of interest is the differences that exist between the matched-pairs data.

To explain how to get to this answer, let's first understand what dependent samples are. Dependent samples refer to data collected from the same individuals or objects, under different conditions or at different times. In such cases, the individual or object serves as their own control group.

When conducting a hypothesis test on dependent samples, we are interested in determining whether there is a significant difference between the two conditions or times for each individual or object. Therefore, the variable of interest is the difference between the paired measurements.

For example, suppose we want to test if a weight loss program is effective. We measure the weights of individuals before and after the program. The variable of interest would be the differences in weight (after - before) for each individual.

By comparing these differences, we can assess whether the weight loss program had a significant effect on the individuals.