Researchers articulate the expected relationships between the variables by the _______.

The correct answer is the null hypothesis. In research, the null hypothesis serves a specific role by articulating a statement of no effect or no relationship between variables. It establishes a baseline or a baseline assumption that can be tested against observed data. Researchers use the null hypothesis to determine whether there is enough statistical evidence to suggest that an alternative hypothesis—which proposes an expected relationship or effect—might be true.

In contrast, the alternative hypothesis explicitly states the expected relationship or effect that the researcher anticipates observing. While the alternative hypothesis is crucial for hypothesis testing, it is not the one that articulates the expected state when researchers commence their investigation; rather, it is the null hypothesis that is being tested for statistical significance.

Parameters refer to numerical values that summarize characteristics of a population and do not address the relationships between variables directly. Statistics are measures calculated from sample data used in hypothesis testing and are not declarations about relationships among variables. Therefore, the null hypothesis is essential in guiding researchers in understanding whether their expected relationships hold true in the context of their study.