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.

Performing a Chi-Square Independence Test In Exercises 13–28, perform the indicated chi-square independence test by performing the steps below.

a. Identify the claim and state H₀ and Hₐ

b. Determine the degrees of freedom, find the critical value, and identify the rejection region.

c. Find the chi-square test statistic.

d. Decide whether to reject or fail to reject the null hypothesis.

e. Interpret the decision in the context of the original claim.

Use the contingency table and expected frequencies from Exercise 8. At α=0.05, test the hypothesis that the variables are dependent.

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?