SECTION 10.2 Independence 543 12. Age Type of movie rented 18 – 24 25 – 34 35 – 44 45 – 64 65 and older Comedy 38 30 24 10 8 Action 15 17 16 9 5 Drama 12 11 19 25 13 Using and Interpreting Concepts 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. 13. Use the contingency table and expected frequencies from Exercise 7. At a = 0.01, test the hypothesis that the variables are independent. 14. Use the contingency table and expected frequencies from Exercise 8. At a = 0.05, test the hypothesis that the variables are dependent. 15. Musculoskeletal Injury The contingency table shows the results of a random sample of patients with pain from musculoskeletal injuries treated with acetaminophen or ibuprofen. At a = 0.10, can you conclude that the treatment is related to the result? (Adapted from American Academy of Pediatrics) Treatment Result Acetaminophen Ibuprofen Significant improvement 58 81 Slight improvement 42 19 16. Attitudes About Safety The contingency table shows the results of a random sample of students by type of school and their attitudes on safety steps taken by the school staff. At a = 0.01, can you conclude that attitudes about the safety steps taken by the school staff are related to the type of school? (Adapted from Horatio Alger Association) School staff has Type of school Taken all steps necessary for student safety Taken some steps toward student safety Public 40 51 Private 64 34
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