13. Chi-Square Tests & Goodness of Fit

Which of the following accurately describes the $\chi ²$ test for independence?

In the context of the $\chi 2^{}$ Test for Independence, what does the test allow us to determine about the relationship between two categorical variables based on experimental observations?

In a chi-square test for independence, how does the difference between the expected frequency $fe$ and the observed frequency $fo$ affect the value of the chi-square statistic?

In the context of a chi-square test for independence, what does a large value of the $\chi 2^{}$ statistic indicate about the relationship between the two categorical variables being tested?