Question

Problem 2. There is a great deal of folklore about the effects of the full moon on humans and other animals. Do animals bite humans more during a full moon? In an attempt to study this question, Bhattacharjee et al (2000) collected data on admissions to a medical facility for treatment of bites by animals: cats, rats, horses, and dogs. 95% of the bites were by man's best friend, the dog. The lunar cycle was divided into 10 periods, and the number of bites in each period is shown in the following table. Day 29 is the full moon. Is there a temporal trend in the incidence of bites? Lunar Day Number of bites 16, 17, 18 137 19, 20, 21 22,23,24 150 163 25, 26, 27 28, 29, 1 201 Answer the question using the likelihood ratio test for the multinomial 269 2,3,4 155 5, 6, 7 142 8, 9, 10 146 11, 12, 13 14, 15 148 110

Answer 1

dudion Jiven that k1o : l0 -) df b = Hypothe sis is gven by tcmporal tuoc 'n the Ho There ís no incident ot bites temporal tundl in The Ha There 1s a ncident ot bit chi- squau Coitical valu ;- above valeus trom the Bry using chi- squau Ctical velue tabl Lyiectkeal 16-19) 16-919

Re quixed bind pected uqurxies : No of .Bita obsevvcd Lunar o-E) =nxP(a) dory P ( 162 1P() (0) 5.6167 319 010345 164 69 IG.14118 shal.a 164-69 150 98- o-1312 o-10345 167-69 22,L3 2L 6-G169 20) 164 69 O-(0345 25,26, 21 CI-2070 6-69 sheol a 163.69 269 28.29,1 0-9603 -10345 1 5 2 3 3-935 16-69 O 10345 142 5 C,7 167.6 1-80S4 0-10345 8,9,1b 2-311 O10345 1,12,13 148 ).93 O-OGE94 I4,15 387Q-0 85-4794 0: 162 2Pl):) The chi-squae test statstics (o- x85.49

3 The test stactstics valuu talh in the sejection vegion pothesis, theufoxe , it can be conclude ujcct the nul SO that the animal bites mou na dap Be cause thc chi- squae contoibution Gl-2010 is mou tn thesc the mOoD unor dors. Thus in the ju bites au moe