\fSPHU 3160 - BIOSTATISTICS IN PUBLIC HEALTH Practice Problem Set XII From Gerstman, Burt B. Basic Biostatistics: Statistics for Public Health Practice, 2nd Edition, Jones & Barlett Learning, 2015. 1. Exercise 18.8, page 483 Table 18.7, page 471 Drove or rode in a car or other vehicle when driver was drinking alcohol within past 30 days by racial/ethnic group. Oi + Total (Ei) Non-Hisp 243 1911 2154 White (218.24) (1935.76) Non-Hisp 25 483 508 Black (51.47) (456.53) Hispanic 55 471 526 (53.29) (472.71) Total 323 2865 3188 H 0 : p1 p 2 p3 vs H 0 : at least two pi differ X1 243 .1128 n1 2154 X 25 p2 2 .0492 n 2 508 X 55 p3 3 .1046 n 3 526 n1 = 2154, X1 =243, p1 n2 = 508, X2 =25, n3 = 526, X3 =55, E1 2154 323 218.24 3188 508 323 51.47 E3 , 3188 526 323 53.29 E5 , 3188 , E2 2154 2865 1935.76 3188 508 2865 456.53 E4 3188 526 2865 472.71 E6 3188 1 SPHU 3160 - BIOSTATISTICS IN PUBLIC HEALTH 6 O E 2 i 2 i Test Statistic Ei i 1 2 2 2 2 = 243 218.24 + 1911 1935.76 + 25 51.47 + 483 456.53 218.24 1935.76 51.47 2 + 55 53.29 + 471 472.71 53.29 471 456.53 2 = 2.8091 + 0.3167 + 13.6130 + 1.5348 + 0.0549 + 0.0062 = 18.33 df = (r-1)(c-1) = (3-1)(2-1) =2 p-value = P( 2df 18.33 ) < .0005, since for =.0005 2 value in Table E, page 493, for 2 degrees of freedom. 2 15.20 is the largest Reject H0 2 SPHU 3160 - BIOSTATISTICS IN PUBLIC HEALTH 2. Exercise 18.9, page 483 a. Table 18.8, page 471 Oi (Ei) CMV+ Restenosed 21 (15.0267) 2 (7.9733) 23 CMVTotal H 0 : p1 p 2 E1 E3 Total 49 26 75 vs H 0 : p1 p 2 49 23 15.0267 75 26 23 7.9733 75 Test Statistic = Did not restenose 28 (33.9733) 24 (18.0267) 52 , E2 , E4 49 52 33.9733 75 26 52 18.0267 75 4 O E 2 i 2 i Ei i 1 21 15.0267 2 + 28 2 7.9733 2 + 24 18.0267 2 33.9733 2 + 33.9733 7.9733 18.0267 15.0267 = 2.3745 + 1.0502 + 4.4750 + 1.9793 = 9.88 df = (r-1)(c-1) = (2-1)(2-1) =1 2 p-value = P( 1df 9.88 ) .001 < p-value < .005, since for =.005 2 7.88 , and for =.001 2 10.83 , Reject H0 3 SPHU 3160 - BIOSTATISTICS IN PUBLIC HEALTH X1 21 .4286 n1 49 X2 2 .0769 n2 = 26, X2 =2, p 2 n 2 26 X X2 21 2 23 p 1 .3067 ; q 1 n1 n 2 49 26 75 b. n1 = 49, X1 =21, p1 p 1 .3067 .6933 H0: p1=p2 vs Ha: p1p2 Test Statistic: Z p1 p 2 1 1 pq n n 1 2 .4286 .0769 1 1 49 26 .3067 .6933 .3517 .3517 .012517765 .11188 = 3.1435 P value = 2 P( Z > 3.14) = 2(.0008) = .0016. Reject H0. Equivalence: Z 2 2 (3.1435)2 = 9.88 4