Question

2. (20 points) Test if a person's political affiliation and their opinion on a tax reform bill are dependent at a 5% level of significance. Favor 125 Democrat Indifferent 82 78 Opposed 85 93 Republican 78

Answer 1

85 and Answer - aiven the table of pearson's political affilation and their opinion on a tax reform bill - favor (3) Indifferent (B) opposed (R. Democrat (A) 125 82 Rebublicam (A2) 78 78 | 93 To test that a pearson's affiliation on their opinion on a tax reform bill are dependent at a 51 level of significance We set null hypothesis Hoi person's affiliation and their opinion on a tas reform bill are independent. against the alternative hypothesis Hi: person's affiliation and their opinion on a ten reform bill are dependent Test statistic is S(A, B j) - (A, B.;). DU in ith in ith where (AiBjle is expected frequency row and jth column (Ai Bj) is observed frequency row and ith column. (Ai BjJe = (A i) (Bj) where N = & Bil = 3 / Bj

Table of observe B . Ai Bj frequencies Total B AU 82 12.5 78 T 203 85 93 292 249 Az 78 Total 160 178 541 Table of expected frequences Ail Bj , Bi | B₂ , B3 I Total AI I 109.6 86.4 96.1 292.1 ~ 292 81.9 73.6 248.9 ~ zug 93.4 203 1 178 Total T sul =N 160 (A, Bi) e = = CAD CB1) - 292 X 203-100 109.6 2 = 541 N (A, B2) e CAD(B₂) - 292 X 160 - 86.4 - 541 Α, (A,B)e (A, B1). (A282)e (A, B)e 541 zug X 203 S41 =93-4 N - (Au) (Bg) - 292 *178_ - (93) (6) - 249 x 202_ - (A2) CB.) - 249 x 160 - 73.6 - (An) CB3) - 249 X 17881.9 S4 sui

Ч ия (A i Bylo . [AiBjlo -AiBi): 4 (AiBi Class (A,B) A 125 (A, B2) - 82 (A, B3) 85 (Az Bi) (A, B2) 78 A₂ B3) bi ga 0.22 Ai Bje 109.6 86.4 96.1 93.4 73-6 3-819 78 1-28 2.54 0.26 1.50 x² = Ě Ě Į (AiBjje - (A i Biley I got (Ai Bjle = 7.96 no Tabulated value of x² at st. significa -nce level and dif = (1-1) (1-1) = (2-1) (3-1) 1 X2 S = 2 is given as X2160.05) = 5.991 since X cal > x 2 (0:05) Hence we reject. Ho at st. level of significance and conclude that person's affiliation and their opinion one taxe reform bill is dependent.