Question

Winning-team data were collected for teams in different sports, with the results given in the accompanying table. Use a 0.05 significance to test the claim that home/ visitor wins are independent of the sport.

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4-Winning-team data were collected for teams in different sports, with the results given in the accompanying table. Use a 0.05 significance to test the claim that homel visitor wins are independent of the sport. Home team wins Basketball Baseball Hockey Football 127 53 50 57 Visiting team wins Basketball Baseball Hockey Football 71 47 43 42

Answer 1

& Solution! – From the gives information, we define two attribute A and B such that A: Homel Vistors (two levels) B: Type of sports (with 4 levels) The gives information can be written in contingency table as follows- B4 (A) B B (Bad B2 (B) B3 CH) Tored Total A (4) 127 53 so 57 287 A (V) 71 47 43 42 203. Total 198 loo 93 99 490 The problem is to test Ho: Home Vistor and type of sport are indepedest. 2 Hi Home Visitor & type of sport ore dependent. Test statistica 2² - Ž 0; 2 i=1 = Eij where Oij = observed free. Eij = Expected freg. = (Row total) (column to tas) N = Total freq = 490 To find this value we prepare the table as follows- Eij so no. of 2 - کلہا 30 Oi 2 / Ei X car 494.7371-490 127 115.9714 139.0774 4.737) 53 S8.5714 47.9586 Critical value- At st los 54.4714 45.8956 Xm-1)(n-1) = x²(2-0 (4-12 57 57.9857 56.0310 x 7.815 hercel) 71 82.0286 61.4542 where ma 47 41.4286 53.3206 Do. of Columns = 4 43 38.528647.9903 Decision: – As Xca xz, 42 41. 0143 43. oog4 we accept Ho at stlas 490 494.7371 Decon - Conclusion! - There is sufficient evidence to conclude that Home / visitors and type of sport are independest. na Total Tab