SECTION 10.2 Independence 547 31. Is the chi-square homogeneity of proportions test a left-tailed, right-tailed, or two-tailed test? 32. Explain how the chi-square independence test is different from the chi-square homogeneity of proportions test. Contingency Tables and Relative Frequencies In Exercises 33–36, use the information below. The frequencies in a contingency table can be written as relative frequencies by dividing each frequency by the sample size. The contingency table below shows the number of U.S. adults (in millions) ages 25 and over by employment status and educational attainment. (Adapted from U.S. Census Bureau) Educational attainment Status Not a high school graduate High school graduate Some college, no degree Associate’s, bachelor’s, or advanced degree Employed 8.3 32.9 19.7 74.6 Unemployed 0.8 2.0 1.1 2.4 Not in civilian labor force 11.1 26.6 13.2 30.3 33. Rewrite the contingency table using relative frequencies. 34. Explain why you cannot perform the chi-square independence test on these data. 35. What percent of U.S. adults ages 25 and over (a) have a degree and are unemployed and (b) have some college education, but no degree, and are not in the civilian labor force? 36. What percent of U.S. adults ages 25 and over (a) are employed and are only high school graduates, (b) are not in the civilian labor force, and (c) are not high school graduates? Conditional Relative Frequencies In Exercises 37 –42, use the contingency table from Exercises 33–36, and the information below. Relative frequencies can also be calculated based on the row totals (by dividing each row entry by the row’s total) or the column totals (by dividing each column entry by the column’s total). These frequencies are conditional relative frequencies and can be used to determine whether an association exists between two categories in a contingency table. 37. Calculate the conditional relative frequencies in the contingency table based on the row totals. 38. What percent of U.S. adults ages 25 and over who are employed have a degree? 39. What percent of U.S. adults ages 25 and over who are not in the civilian labor force have some college education, but no degree? 40. Calculate the conditional relative frequencies in the contingency table based on the column totals. 41. What percent of U.S. adults ages 25 and over who have a degree are not in the civilian labor force? 42. What percent of U.S. adults ages 25 and over who are not high school graduates are unemployed?
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