540 CHAPTER 10 Chi-Square Tests and the F -Distribution The contingency table has two rows and five columns, so the chi-square distribution has d.f. = 1r - 121c - 12 = 12 - 1215 - 12 = 4 degrees of freedom. Because d.f. = 4 and a = 0.01, the critical value is x 2 0 = 13.277. The rejection region is x 2 7 13.277. You can use a table to find the chi-square test statistic, as shown below. O E O − E 1O − E22 1O − E22 E 190 163.622 26.378 695.798884 4.252477564 39 28.794 10.206 104.162436 3.617504897 97 102.142 -5.142 26.440164 0.258856925 43 76.266 -33.266 1106.626756 14.510093043 17 15.175 1.825 3.330625 0.219481054 651 677.378 -26.378 695.798884 1.027194394 109 119.206 -10.206 104.162436 0.873801956 428 422.858 5.142 26.440164 0.062527288 349 315.734 33.266 1106.626756 3.504933761 61 62.825 -1.825 3.330625 0.053014326 x 2 = Σ1O - E22 E ≈ 28.380 The figure at the right shows the location of the rejection region and the chi-square test statistic. Because x 2 ≈ 28.380 is in the rejection region, you reject the null hypothesis. Interpretation There is enough evidence at the 1% level of significance to conclude that the student’s living arrangement depends on family college experience. TRY IT YOURSELF 2 The contingency table shows the results of a random sample of 1996 undergraduate students classified by their living arrangement and whether they borrowed money to pay for college. At a = 0.01, can you conclude that the variables student’s living arrangement and borrowing status are related? (The expected frequencies are displayed in parentheses.) Student’s living arrangement Borrowing status With parents, rent free With parents, pay rent On campus Off campus, w/others Off campus, alone Total Borrowed 364 (426.549) 92 (75.451) 303 (271.120) 203 (195.669) 42 (35.210) 1004 Did not borrow 484 (421.451) 58 (74.549) 236 (267.880) 186 (193.331) 28 (34.790) 992 Total 848 150 539 389 70 1996 Answer: Page A42 5 1015202530 0 2χ = 13.277 2χ = 28.380 α= 0.01 Rejection region 2χ
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