13. Chi-Square Tests & Goodness of Fit

Does the Treatment Affect Success? The following table lists frequencies of successes and failures for different treatments used for a stress fracture in a foot bone (based on data from “Surgery Unfounded for Tarsal Navicular Stress Fracture,” by Bruce Jancin, Internal Medicine News, Vol. 42, No. 14). Use a 0.05 significance level to test the claim that success of the treatment is independent of the type of treatment. What does the result indicate about the increasing trend to use surgery?

Explain why the chi-square independence test is always a right-tailed test.

True or False? In Exercises 5 and 6, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

If the two variables in a chi-square independence test are dependent, then you can expect little difference between the observed frequencies and the expected frequencies.

True or False? In Exercises 5 and 6, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

When the test statistic for the chi-square independence test is large, you will, in most cases, reject the null hypothesis.

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?

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?