Which of the following would be an appropriate null hypothesis in a chi square test of independence?

In a chi-square test of independence, the null hypothesis specifically states that there is no association or relationship between the two categorical (nominal) variables being analyzed. This means that any observed differences in the frequencies of the categories can be attributed to random chance rather than a true relationship between the variables.

Stating that there is no relationship aligns with the foundational principle of hypothesis testing, where the null hypothesis serves as a default position that assumes a lack of effect or relationship until evidence suggests otherwise. By contrasting this with the alternative hypothesis, which posits that a significant relationship does exist, researchers can use statistical analysis to determine whether to reject the null hypothesis based on the data.

This framework is essential to interpreting the results of the chi-square test, as it helps to establish the context for understanding the relationship between the variables in question. This methodology ensures that any conclusions drawn are based on objective analysis rather than assumptions.